Daily Papers

Vision-Language-Action (VLA) models have achieved impressive performance on diverse embodied tasks. However, deploying VLA models on low-power onboard devices, such as the Jetson Orin, remains challenging due to their high computational complexity, which leads to substantial inference latency and low control frequency. Asynchronous inference can partially mask this latency by parallelizing action execution and subsequent inference, but it introduces two critical issues: perception-execution misalignment and long reaction time. In this paper, we propose Jetson-PI, a method for efficient VLA deployment on onboard devices via Foresight-Aligned Asynchronous Correction. To address misalignment, we train a lightweight future correction module that predicts future environment representation conditioned on committed actions, enabling the action expert to directly predict actions from the future time step. To reduce reaction time, we introduce confidence-based scheduling optimization that adaptively balances VLM and action expert invocations, complemented by system-level accelerations including CUDA graph reuse, GPU-resident intermediate buffering, and flow unrolling. Extensive experiments demonstrate that Jetson-PI achieves 8.66x and 5.41x improvements in control frequency compared with naive PyTorch and vla.cpp on NVIDIA Jetson Orin, while outperforming VLASH by 14.8\% in average success rate on the LIBERO benchmark. The code of our asynchronous algorithm is available on https://github.com/PKU-SEC-Lab/Jetson-PI, and our efficient llama.cpp-based inference engine is available on https://github.com/PKU-SEC-Lab/Jetson-PI-Edge.

Generative machine learning methods, such as diffusion models and flow matching, have shown great potential in modeling complex system behaviors and building efficient surrogate models. However, these methods typically learn the underlying physics implicitly from data. We propose Physics-Based Flow Matching (PBFM), a novel generative framework that explicitly embeds physical constraints, both PDE residuals and algebraic relations, into the flow matching objective. We also introduce temporal unrolling at training time that improves the accuracy of the final, noise-free sample prediction. Our method jointly minimizes the flow matching loss and the physics-based residual loss without requiring hyperparameter tuning of their relative weights. Additionally, we analyze the role of the minimum noise level, sigma_{min}, in the context of physical constraints and evaluate a stochastic sampling strategy that helps to reduce physical residuals. Through extensive benchmarks on three representative PDE problems, we show that our approach yields up to an 8times more accurate physical residuals compared to FM, while clearly outperforming existing algorithms in terms of distributional accuracy. PBFM thus provides a principled and efficient framework for surrogate modeling, uncertainty quantification, and accelerated simulation in physics and engineering applications.

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains challenging, as naive gradient-based optimization requires backpropagating through numerical solvers and often leads to instability. Existing approaches typically address this issue by restricting the expressive capacity of flow-based policies, resulting in a trade-off between optimization stability and representational flexibility. To resolve this, we introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate terminal trajectory value to intermediate latent states along the policy-induced flow. This formulation enables stable policy optimization using intermediate value gradients without unrolling the numerical solver, effectively bridging the gap between stability and expressivity. We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points, while also enabling stable online adaptation within the same framework.

Egocentric action anticipation consists in understanding which objects the camera wearer will interact with in the near future and which actions they will perform. We tackle the problem proposing an architecture able to anticipate actions at multiple temporal scales using two LSTMs to 1) summarize the past, and 2) formulate predictions about the future. The input video is processed considering three complimentary modalities: appearance (RGB), motion (optical flow) and objects (object-based features). Modality-specific predictions are fused using a novel Modality ATTention (MATT) mechanism which learns to weigh modalities in an adaptive fashion. Extensive evaluations on two large-scale benchmark datasets show that our method outperforms prior art by up to +7% on the challenging EPIC-Kitchens dataset including more than 2500 actions, and generalizes to EGTEA Gaze+. Our approach is also shown to generalize to the tasks of early action recognition and action recognition. Our method is ranked first in the public leaderboard of the EPIC-Kitchens egocentric action anticipation challenge 2019. Please see our web pages for code and examples: http://iplab.dmi.unict.it/rulstm - https://github.com/fpv-iplab/rulstm.

Training expressive flow-based policies with off-policy reinforcement learning is notoriously unstable due to gradient pathologies in the multi-step action sampling process. We trace this instability to a fundamental connection: the flow rollout is algebraically equivalent to a residual recurrent computation, making it susceptible to the same vanishing and exploding gradients as RNNs. To address this, we reparameterize the velocity network using principles from modern sequential models, introducing two stable architectures: Flow-G, which incorporates a gated velocity, and Flow-T, which utilizes a decoded velocity. We then develop a practical SAC-based algorithm, enabled by a noise-augmented rollout, that facilitates direct end-to-end training of these policies. Our approach supports both from-scratch and offline-to-online learning and achieves state-of-the-art performance on continuous control and robotic manipulation benchmarks, eliminating the need for common workarounds like policy distillation or surrogate objectives.

Normalizing Flows (NFs) are widely used in deep generative models for their exact likelihood estimation and efficient sampling. However, they require substantial memory since the latent space matches the input dimension. Multi-scale architectures address this by progressively reducing latent dimensions while preserving reversibility. Existing multi-scale architectures use simple, static channel-wise splitting, limiting expressiveness. To improve this, we introduce a regularized, feature-dependent Shuffle operation and integrate it into vanilla multi-scale architecture. This operation adaptively generates channel-wise weights and shuffles latent variables before splitting them. We observe that such operation guides the variables to evolve in the direction of entropy increase, hence we refer to NFs with the Shuffle operation as Entropy-Informed Weighting Channel Normalizing Flow (EIW-Flow). Extensive experiments on CIFAR-10, CelebA, ImageNet, and LSUN demonstrate that EIW-Flow achieves state-of-the-art density estimation and competitive sample quality for deep generative modeling, with minimal computational overhead.

Streaming video generation, as one fundamental component in interactive world models and neural game engines, aims to generate high-quality, low-latency, and temporally coherent long video streams. However, most existing work suffers from severe error accumulation that often significantly degrades the generated stream videos over long horizons. We design Rolling Forcing, a novel video generation technique that enables streaming long videos with minimal error accumulation. Rolling Forcing comes with three novel designs. First, instead of iteratively sampling individual frames, which accelerates error propagation, we design a joint denoising scheme that simultaneously denoises multiple frames with progressively increasing noise levels. This design relaxes the strict causality across adjacent frames, effectively suppressing error growth. Second, we introduce the attention sink mechanism into the long-horizon stream video generation task, which allows the model to keep key value states of initial frames as a global context anchor and thereby enhances long-term global consistency. Third, we design an efficient training algorithm that enables few-step distillation over largely extended denoising windows. This algorithm operates on non-overlapping windows and mitigates exposure bias conditioned on self-generated histories. Extensive experiments show that Rolling Forcing enables real-time streaming generation of multi-minute videos on a single GPU, with substantially reduced error accumulation.

We propose Delta Velocity Rectified Flow (DVRF), a novel inversion-free, path-aware editing framework within rectified flow models for text-to-image editing. DVRF is a distillation-based method that explicitly models the discrepancy between the source and target velocity fields in order to mitigate over-smoothing artifacts rampant in prior distillation sampling approaches. We further introduce a time-dependent shift term to push noisy latents closer to the target trajectory, enhancing the alignment with the target distribution. We theoretically demonstrate that when this shift is disabled, DVRF reduces to Delta Denoising Score, thereby bridging score-based diffusion optimization and velocity-based rectified-flow optimization. Moreover, when the shift term follows a linear schedule under rectified-flow dynamics, DVRF generalizes the Inversion-free method FlowEdit and provides a principled theoretical interpretation for it. Experimental results indicate that DVRF achieves superior editing quality, fidelity, and controllability while requiring no architectural modifications, making it efficient and broadly applicable to text-to-image editing tasks. Code is available at https://github.com/gaspardbd/DeltaVelocityRectifiedFlow.

Recent flow cessation experiments on soft materials have shown a counter-intuitive non-monotonic relaxation of the shear stress: following the switch-off of a steady imposed shear flow, the stress initially decays before later increasing again. By simulating the soft glassy rheology model in a form extended to allow steady state shear banding, we show that the presence of shear bands prior to flow cessation can give rise to this phenomenon. We give a mechanistic understanding of the basic physics involved, in terms of (i) the decay of the shear bands after flow cessation, and (ii) the evolution of frustrated local stresses, governed by different time scales for plastic relaxation in each band. In particular, an elastic recoil in the unsheared band gives rise to negative local frustrated stresses, the slow release of which can cause an increase in macroscopic stress. Given that shear banding and frustrated local stresses arise widely across disordered soft solids, we argue that non-monotonic stress relaxation after flow cessation may occur in many different materials.

Many training data attribution (TDA) methods aim to estimate how a model's behavior would change if one or more data points were removed from the training set. Methods based on implicit differentiation, such as influence functions, can be made computationally efficient, but fail to account for underspecification, the implicit bias of the optimization algorithm, or multi-stage training pipelines. By contrast, methods based on unrolling address these issues but face scalability challenges. In this work, we connect the implicit-differentiation-based and unrolling-based approaches and combine their benefits by introducing Source, an approximate unrolling-based TDA method that is computed using an influence-function-like formula. While being computationally efficient compared to unrolling-based approaches, Source is suitable in cases where implicit-differentiation-based approaches struggle, such as in non-converged models and multi-stage training pipelines. Empirically, Source outperforms existing TDA techniques in counterfactual prediction, especially in settings where implicit-differentiation-based approaches fall short.

Recent inversion-free, flow-based image editing methods such as FlowEdit leverages a pre-trained noise-to-image flow model such as Stable Diffusion 3, enabling text-driven manipulation by solving an ordinary differential equation (ODE). While the lack of exact latent inversion is a core advantage of these methods, it often results in unstable editing trajectories and poor source consistency. To address this limitation, we propose {\em FlowAlign}, a novel inversion-free flow-based framework for consistent image editing with optimal control-based trajectory control. Specifically, FlowAlign introduces source similarity at the terminal point as a regularization term to promote smoother and more consistent trajectories during the editing process. Notably, our terminal point regularization is shown to explicitly balance semantic alignment with the edit prompt and structural consistency with the source image along the trajectory. Furthermore, FlowAlign naturally supports reverse editing by simply reversing the ODE trajectory, highliting the reversible and consistent nature of the transformation. Extensive experiments demonstrate that FlowAlign outperforms existing methods in both source preservation and editing controllability.

Machine unlearning aims to remove knowledge of the specific training data in a well-trained model. Currently, machine unlearning methods typically handle all forgetting data in a single batch, removing the corresponding knowledge all at once upon request. However, in practical scenarios, requests for data removal often arise in a streaming manner rather than in a single batch, leading to reduced efficiency and effectiveness in existing methods. Such challenges of streaming forgetting have not been the focus of much research. In this paper, to address the challenges of performance maintenance, efficiency, and data access brought about by streaming unlearning requests, we introduce a streaming unlearning paradigm, formalizing the unlearning as a distribution shift problem. We then estimate the altered distribution and propose a novel streaming unlearning algorithm to achieve efficient streaming forgetting without requiring access to the original training data. Theoretical analyses confirm an O(T + V_T) error bound on the streaming unlearning regret, where V_T represents the cumulative total variation in the optimal solution over T learning rounds. This theoretical guarantee is achieved under mild conditions without the strong restriction of convex loss function. Experiments across various models and datasets validate the performance of our proposed method.

Optical flow is a fundamental technique for motion estimation, widely applied in video stabilization, interpolation, and object tracking. Traditional optical flow estimation methods rely on restrictive assumptions like brightness constancy and slow motion constraints. Recent deep learning-based flow estimations require extensive training on large domain-specific datasets, making them computationally demanding. Also, artificial intelligence (AI) advances have enabled deep learning models to take advantage of optical flow as an important feature for object tracking and motion analysis. Since optical flow is commonly encoded in HSV for visualization, its conversion to RGB for neural network processing is nonlinear and may introduce perceptual distortions. These transformations amplify the sensitivity to estimation errors, potentially affecting the predictive accuracy of the networks. To address these challenges that are influential to the performance of downstream network models, we propose Reynolds flow, a novel training-free flow estimation inspired by the Reynolds transport theorem, offering a principled approach to modeling complex motion dynamics. In addition to conventional HSV-based visualization of Reynolds flow, we also introduce an RGB-encoded representation of Reynolds flow designed to improve flow visualization and feature enhancement for neural networks. We evaluated the effectiveness of Reynolds flow in video-based tasks. Experimental results on three benchmarks, tiny object detection on UAVDB, infrared object detection on Anti-UAV, and pose estimation on GolfDB, demonstrate that networks trained with RGB-encoded Reynolds flow achieve SOTA performance, exhibiting improved robustness and efficiency across all tasks.

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier-Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.

Large Language Models memorize vast amounts of training data, raising concerns regarding privacy, copyright infringement, and safety. Machine unlearning seeks to remove the influence of a targeted forget set while preserving model performance, ideally approximating a model retrained from scratch without the forget set. Existing approaches aim to achieve this by updating model parameters via gradient-based methods. However, these updates are computationally expensive, lead to irreversible weight changes, and degrade when the model is quantized for deployment. A recent alternative to changing model weights is activation engineering, where activations are changed during inference to steer model behavior. Despite circumventing weight editing, naive activation steering introduces its own failure modes, as a single global steering vector applies the same intervention to every input, leading to unintended changes in model behavior. We introduce Inference-Time Unlearning via Gated Activation Redirection (GUARD-IT), a training- and gradient-free method that unlearns via input-dependent activation steering at inference time. The resulting intervention is applied as a norm-preserving rotation in the residual stream, leaving model weights untouched. Experiments on TOFU and MUSE show that GUARD-IT matches or exceeds 12 gradient-based baselines across three model scales, while being the only method to simultaneously preserve utility, suppress memorization, and avoid catastrophic collapse across all settings. GUARD-IT further supports continual unlearning without retraining, and remains effective under quantization, a scenario in which parameter-editing methods degrade.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.

Recently, autoregressive (AR) video diffusion models has achieved remarkable performance. However, due to their limited training durations, a train-test gap emerges when testing at longer horizons, leading to rapid visual degradations. Following Self Forcing, which studies the train-test gap within the training duration, this work studies the train-test gap beyond the training duration, i.e., the gap between the limited horizons during training and open-ended horizons during testing. Since open-ended testing can extend beyond any finite training window, and long-video training is computationally expensive, we pursue a training-free solution to bridge this gap. To explore a training-free solution, we conduct a systematic analysis of AR cache maintenance. These insights lead to Rolling Sink. Built on Self Forcing (trained on only 5s clips), Rolling Sink effectively scales the AR video synthesis to ultra-long durations (e.g., 5-30 minutes at 16 FPS) at test time, with consistent subjects, stable colors, coherent structures, and smooth motions. As demonstrated by extensive experiments, Rolling Sink achieves superior long-horizon visual fidelity and temporal consistency compared to SOTA baselines. Project page: https://rolling-sink.github.io/

Mitigating the retention of sensitive or private information in large language models is essential for enhancing privacy and safety. Existing unlearning methods, like Gradient Ascent and Negative Preference Optimization, directly tune models to remove unwanted information. However, these methods often become unstable because they fine-tune by maximizing cross-entropy loss, which is the opposite of traditional loss minimization in learning. This reversal creates instability, especially on larger datasets, as the model struggles to balance unlearning with maintaining language capacity, leading to over-unlearning. In this paper, we introduce UnDIAL (Unlearning via Self-Distillation on Adjusted Logits), a novel and robust unlearning method. Our approach leverages self-distillation to adjust logits and selectively reduce the influence of targeted tokens. This technique ensures smooth convergence and avoids catastrophic forgetting, even in challenging unlearning tasks with large datasets and sequential unlearning requests. Extensive experiments show that UnDIAL can achieve both robustness in unlearning and scalability while maintaining stable training dynamics and resilience to hyperparameter tuning.

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

Flow Matching (FM) constructs linear conditional probability paths, but the learned marginal velocity field inevitably exhibits strong curvature due to trajectory superposition. This curvature severely inflates numerical truncation errors, bottlenecking few-step sampling. To overcome this, we introduce Isokinetic Flow Matching (Iso-FM), a lightweight, Jacobian-free dynamical regularizer that directly penalizes pathwise acceleration. By using a self-guided finite-difference approximation of the material derivative Dv/Dt, Iso-FM enforces local velocity consistency without requiring auxiliary encoders or expensive second-order autodifferentiation. Operating as a pure plug-and-play addition to single-stage FM training, Iso-FM dramatically improves few-step generation. On CIFAR-10 (DiT-S/2), Iso-FM slashes conditional non-OT FID at 2 steps from 78.82 to 27.13 - a 2.9x relative efficiency gain - and reaches a best-observed FID at 4 steps of 10.23. These results firmly establish acceleration regularization as a principled, compute-efficient mechanism for fast generative sampling.

Video Diffusion Models (VDMs) can generate high-quality videos, but often struggle with producing temporally coherent motion. Optical flow supervision is a promising approach to address this, with prior works commonly employing warping-based strategies that avoid explicit flow matching. In this work, we explore an alternative formulation, FlowLoss, which directly compares flow fields extracted from generated and ground-truth videos. To account for the unreliability of flow estimation under high-noise conditions in diffusion, we propose a noise-aware weighting scheme that modulates the flow loss across denoising steps. Experiments on robotic video datasets suggest that FlowLoss improves motion stability and accelerates convergence in early training stages. Our findings offer practical insights for incorporating motion-based supervision into noise-conditioned generative models.

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned, autoregressive models. However, the intricacies of turbulence in three dimensions necessitate training these models with very small time steps, while generating realistic flow states requires either long roll-outs with many steps and significant error accumulation or starting from a known, realistic flow state - something we aimed to avoid in the first place. Instead, we propose to approach turbulent flow simulation as a generative task directly learning the manifold of all possible turbulent flow states without relying on any initial flow state. For our experiments, we introduce a challenging 3D turbulence dataset of high-resolution flows and detailed vortex structures caused by various objects and derive two novel sample evaluation metrics for turbulent flows. On this dataset, we show that our generative model captures the distribution of turbulent flows caused by unseen objects and generates high-quality, realistic samples amenable for downstream applications without access to any initial state.

One-step generative modeling has emerged as a leading approach for amortizing the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and unbounded gradient variance. In this work, we establish a theory that attributes this pathology to a misuse of the conditional velocity field. We show that the conditional velocity plays two distinct statistical roles in the loss: both as an unbiased regression target and as a Monte Carlo control variate in a Jacobi-vector product, with the original MeanFlow loss assigning the wrong coefficient to the latter. We derive the optimal coefficient in closed form and show that a family of fixes in concurrent works corresponds to different practical realizations of the same optimum. A controlled sweep of this coefficient on two-dimensional benchmarks and on a latent Diffusion Transformer recovers the predicted bias-variance ordering. Our DiT experiment also reveals a quantitative FID-MSE landscape mismatch. Specifically, although the gradient-MSE is minimized at an interior coefficient value near β!=!0.94, the coefficient that minimizes FID prefers to use conditional velocity directly at the unbiased corner. Our analysis therefore explains why MeanFlow is unstable and unifies its concurrent remedies, and shows that the variance-optimal coefficient need not coincide with the quality-optimal one.

Video generation has achieved significant advances through rectified flow techniques, but issues like unsmooth motion and misalignment between videos and prompts persist. In this work, we develop a systematic pipeline that harnesses human feedback to mitigate these problems and refine the video generation model. Specifically, we begin by constructing a large-scale human preference dataset focused on modern video generation models, incorporating pairwise annotations across multi-dimensions. We then introduce VideoReward, a multi-dimensional video reward model, and examine how annotations and various design choices impact its rewarding efficacy. From a unified reinforcement learning perspective aimed at maximizing reward with KL regularization, we introduce three alignment algorithms for flow-based models by extending those from diffusion models. These include two training-time strategies: direct preference optimization for flow (Flow-DPO) and reward weighted regression for flow (Flow-RWR), and an inference-time technique, Flow-NRG, which applies reward guidance directly to noisy videos. Experimental results indicate that VideoReward significantly outperforms existing reward models, and Flow-DPO demonstrates superior performance compared to both Flow-RWR and standard supervised fine-tuning methods. Additionally, Flow-NRG lets users assign custom weights to multiple objectives during inference, meeting personalized video quality needs. Project page: https://gongyeliu.github.io/videoalign.

Flow-based generative models have recently demonstrated strong performance, yet sampling typically relies on expensive numerical integration of ordinary differential equations (ODEs). Rectified Flow enables one-step sampling by learning nearly straight probability paths, but achieving such straightness requires multiple computationally intensive reflow iterations. MeanFlow achieves one-step generation by directly modeling the average velocity over time; however, when trained on highly curved flows, it suffers from slow convergence and noisy supervision. To address these limitations, we propose Rectified MeanFlow, a framework that models the mean velocity field along the rectified trajectory using only a single reflow step. This eliminates the need for perfectly straightened trajectories while enabling efficient training. Furthermore, we introduce a simple yet effective truncation heuristic that aims to reduce residual curvature and further improve performance. Extensive experiments on ImageNet at 64, 256, and 512 resolutions show that Re-MeanFlow consistently outperforms prior one-step flow distillation and Rectified Flow methods in both sample quality and training efficiency. Code is available at https://github.com/Xinxi-Zhang/Re-MeanFlow.

Flow-based methods have achieved significant success in various generative modeling tasks, capturing nuanced details within complex data distributions. However, few existing works have exploited this unique capability to resolve fine-grained structural details beyond generation tasks. This paper presents a flow-inspired framework for representation learning. First, we demonstrate that a rectified flow trained using independent coupling is zero everywhere at t=0.5 if and only if the source and target distributions are identical. We term this property the zero-flow criterion. Second, we show that this criterion can certify conditional independence, thereby extracting sufficient information from the data. Third, we translate this criterion into a tractable, simulation-free loss function that enables learning amortized Markov blankets in graphical models and latent representations in self-supervised learning tasks. Experiments on both simulated and real-world datasets demonstrate the effectiveness of our approach. The code reproducing our experiments can be found at: https://github.com/probabilityFLOW/zfe.

Activation-based control steers large language models (LLMs) by intervening on their internal representations during inference, and has emerged as an effective paradigm for controlling behaviors such as persona and style. However, existing methods often rely on fixed steering directions or task-specific intervention modules, making them difficult to adapt to fine-grained concepts and compositional constraints. We propose UniSteer, a text-guided activation flow matching model that learns a conditional distribution over residual-stream activations from natural-language conditions. Instead of fitting a separate intervention for each target behavior, UniSteer learns a universal conditional velocity field in activation space. At inference time, UniSteer performs flow inversion by partially transporting a source activation toward a latent state and regenerating it under a target textual condition before injecting it back into the frozen LLM. The same conditional model supports activation-space classification by selecting the textual label with the lowest reconstruction energy. Experiments on three target LLMs show that UniSteer provides a unified interface across behavioral control, truthfulness steering, fine-grained concept steering, multi-constraint instruction following, and activation-space classification.

In the last decade many research efforts have been focused on understanding the rheology of disordered materials, and several theoretical predictions have been put forward regarding their yielding behavior. Nevertheless, not many experiments nor molecular dynamics simulations were dedicated to testing those theoretical predictions. Here we use computer simulations to study the yielding transition under two different loading schemes: standard simple shear dynamics, and self-propelled, dense active systems. In the active systems a yielding transition is observed as expected, when the self-propulsion is increased. However, the range of self-propulsions in which a pure liquid regime exist appears to vanish upon approaching the so-called "jamming point" at which solidity of soft-sphere packings is lost. Such an "active yielding" transition shares similarities with the generic yielding transition for shear flows. A Herschel-Bulkley law is observed in both loading scenarios, with a clear difference in the critical scaling exponents between the two, suggesting the existent of different universality classes for the yielding transition under different driving conditions. In addition, we present direct measurements of length and time scales for both driving scenarios. A comparison with theoretical predictions from recent literature reveals poor agreement with our numerical results.

As Large Language Models (LLMs) become increasingly prevalent, their security vulnerabilities have already drawn attention. Machine unlearning is introduced to seek to mitigate these risks by removing the influence of undesirable data. However, existing methods not only rely on the retained dataset to preserve model utility, but also suffer from cumulative catastrophic utility loss under continuous unlearning requests. To solve this dilemma, we propose a novel method, called Rotation Control Unlearning (RCU), which leverages the rotational salience weight of RCU to quantify and control the unlearning degree in the continuous unlearning process. The skew symmetric loss is designed to construct the existence of the cognitive rotation space, where the changes of rotational angle can simulate the continuous unlearning process. Furthermore, we design an orthogonal rotation axes regularization to enforce mutually perpendicular rotation directions for continuous unlearning requests, effectively minimizing interference and addressing cumulative catastrophic utility loss. Experiments on multiple datasets confirm that our method without retained dataset achieves SOTA performance.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Aligning text-to-image flow matching models with human preferences via direct reward backpropagation is sample-efficient but hampered by two well-known pathologies: activations cannot be stored across the full sampling trajectory at modern model scale, and chained Jacobian products across steps inflate the reward gradient as it travels back to early indices. Connector-based methods, such as LeapAlign, address these issues by replacing the full backward trajectory with a short pinned path, highlighting a useful decoupling between sampling and optimization. However, the quality of the resulting gradient depends on how accurately this short path approximates the full rollout, especially over long intervals. We propose FlowBP, a unified surrogate-trajectory framework that treats the backward trajectory itself as the design object. FlowBP keeps a no-gradient cached rollout for sampling, then builds a lightweight backward surrogate from cached and selectively re-forwarded velocities. This view separates four choices: the reward-model input, active set, integration weights, and bridge coupling, and recovers prior direct-gradient methods as particular settings. Within this framework, we instantiate three variants: FlowBP-Sparse uses sparse Euler reconstruction, FlowBP-Bridge adds controlled bridge coupling, and FlowBP-Lagrange raises the order of leap quadrature. All three bound memory by the active-set size and limit gradient chaining to at most one Jacobian factor. Across SD3.5-M, FLUX.1-dev, and FLUX.2-Klein-base on preference, quality, and compositional metrics, the three variants improve over direct-gradient baselines on most metrics.

Few-step video generation has been significantly advanced by consistency distillation. However, the performance of consistency-distilled models often degrades as more sampling steps are allocated at test time, limiting their effectiveness for any-step video diffusion. This limitation arises because consistency distillation replaces the original probability-flow ODE trajectory with a consistency-sampling trajectory, weakening the desirable test-time scaling behavior of ODE sampling. To address this limitation, we introduce AnyFlow, the first any-step video diffusion distillation framework based on flow maps. Instead of distilling a model for only a few fixed sampling steps, AnyFlow optimizes the full ODE sampling trajectory. To this end, we shift the distillation target from endpoint consistency mapping (z_{t}rightarrow z_{0}) to flow-map transition learning (z_{t}rightarrow z_{r}) over arbitrary time intervals. We further propose Flow Map Backward Simulation, which decomposes a full Euler rollout into shortcut flow-map transitions, enabling efficient on-policy distillation that reduces test-time errors (i.e., discretization error in few-step sampling and exposure bias in causal generation). Extensive experiments across both bidirectional and causal architectures, at scales ranging from 1.3B to 14B parameters, demonstrate that AnyFlow achieves performance matches or surpasses consistency-based counterparts in the few-step regime, while scaling with sampling step budgets.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Continuous-time Consistency Models (CMs) promise efficient few-step generation but face significant challenges with training instability. We argue this instability stems from a fundamental conflict: by training a network to learn only a shortcut across a probability flow, the model loses its grasp on the instantaneous velocity field that defines the flow. Our solution is to explicitly anchor the model in the underlying flow during training. We introduce the Flow-Anchored Consistency Model (FACM), a simple but effective training strategy that uses a Flow Matching (FM) task as an anchor for the primary CM shortcut objective. This Flow-Anchoring approach requires no architectural modifications and is broadly compatible with standard model architectures. By distilling a pre-trained LightningDiT model, our method achieves a state-of-the-art FID of 1.32 with two steps (NFE=2) and 1.76 with just one step (NFE=1) on ImageNet 256x256, significantly outperforming previous methods. This provides a general and effective recipe for building high-performance, few-step generative models. Our code and pretrained models: https://github.com/ali-vilab/FACM.

Recent advances in large-scale text-to-image diffusion models have heightened concerns about their potential misuse, especially in generating harmful or misleading content. This underscores the urgent need for effective machine unlearning, i.e., removing specific knowledge or concepts from pretrained models without compromising overall performance. One possible approach is Low-Rank Adaptation (LoRA), which offers an efficient means to fine-tune models for targeted unlearning. However, LoRA often inadvertently alters unrelated content, leading to diminished image fidelity and realism. To address this limitation, we introduce UnGuide -- a novel approach which incorporates UnGuidance, a dynamic inference mechanism that leverages Classifier-Free Guidance (CFG) to exert precise control over the unlearning process. UnGuide modulates the guidance scale based on the stability of a few first steps of denoising processes, enabling selective unlearning by LoRA adapter. For prompts containing the erased concept, the LoRA module predominates and is counterbalanced by the base model; for unrelated prompts, the base model governs generation, preserving content fidelity. Empirical results demonstrate that UnGuide achieves controlled concept removal and retains the expressive power of diffusion models, outperforming existing LoRA-based methods in both object erasure and explicit content removal tasks.

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative models. The main advantage of discriminative models is that they learn a small correction to a starting simulation while generative models scale better to regions of phase space with little data. We propose to use Schroedinger Bridges and diffusion models to create SBUnfold, an unfolding approach that combines the strengths of both discriminative and generative models. The key feature of SBUnfold is that its generative model maps one set of events into another without having to go through a known probability density as is the case for normalizing flows and standard diffusion models. We show that SBUnfold achieves excellent performance compared to state of the art methods on a synthetic Z+jets dataset.

Straightening the probability flow of the continuous-time generative models, such as diffusion models or flow-based models, is the key to fast sampling through the numerical solvers, existing methods learn a linear path by directly generating the probability path the joint distribution between the noise and data distribution. One key reason for the slow sampling speed of the ODE-based solvers that simulate these generative models is the global truncation error of the ODE solver, caused by the high curvature of the ODE trajectory, which explodes the truncation error of the numerical solvers in the low-NFE regime. To address this challenge, We propose a novel method called SeqRF, a learning technique that straightens the probability flow to reduce the global truncation error and hence enable acceleration of sampling and improve the synthesis quality. In both theoretical and empirical studies, we first observe the straightening property of our SeqRF. Through empirical evaluations via SeqRF over flow-based generative models, We achieve surpassing results on CIFAR-10, CelebA-64 times 64, and LSUN-Church datasets.

Pre-trained flow-based models excel at synthesizing complex scenes yet lack a direct mechanism for disentangling and customizing their underlying concepts from one-shot real-world sources. To demystify this process, we first introduce a novel differential probing technique to isolate and analyze the influence of individual concept tokens on the velocity field over time. This investigation yields a critical insight: the generative process is not monolithic but unfolds in three distinct stages. An initial Blueprint Stage establishes low-frequency structure, followed by a pivotal Instantiation Stage where content concepts emerge with peak intensity and become naturally disentangled, creating an optimal window for manipulation. A final concept-insensitive refinement stage then synthesizes fine-grained details. Guided by this discovery, we propose ConceptWeaver, a framework for one-shot concept disentanglement. ConceptWeaver learns concept-specific semantic offsets from a single reference image using a stage-aware optimization strategy that aligns with the three-stage framework. These learned offsets are then deployed during inference via our novel ConceptWeaver Guidance (CWG) mechanism, which strategically injects them at the appropriate generative stage. Extensive experiments validate that ConceptWeaver enables high-fidelity, compositional synthesis and editing, demonstrating that understanding and leveraging the intrinsic, staged nature of flow models is key to unlocking precise, multi-granularity content manipulation.

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.

We propose FlowAnchor, a training-free framework for stable and efficient inversion-free, flow-based video editing. Inversion-free editing methods have recently shown impressive efficiency and structure preservation in images by directly steering the sampling trajectory with an editing signal. However, extending this paradigm to videos remains challenging, often failing in multi-object scenes or with increased frame counts. We identify the root cause as the instability of the editing signal in high-dimensional video latent spaces, which arises from imprecise spatial localization and length-induced magnitude attenuation. To overcome this challenge, FlowAnchor explicitly anchors both where to edit and how strongly to edit. It introduces Spatial-aware Attention Refinement, which enforces consistent alignment between textual guidance and spatial regions, and Adaptive Magnitude Modulation, which adaptively preserves sufficient editing strength. Together, these mechanisms stabilize the editing signal and guide the flow-based evolution toward the desired target distribution. Extensive experiments demonstrate that FlowAnchor achieves more faithful, temporally coherent, and computationally efficient video editing across challenging multi-object and fast-motion scenarios. The project page is available at https://cuc-mipg.github.io/FlowAnchor.github.io/.

Normalising Flows are non-parametric statistical models characterised by their dual capabilities of density estimation and generation. This duality requires an inherently invertible architecture. However, the requirement of invertibility imposes constraints on their expressiveness, necessitating a large number of parameters and innovative architectural designs to achieve good results. Whilst flow-based models predominantly rely on neural-network-based transformations for expressive designs, alternative transformation methods have received limited attention. In this work, we present Ferumal flow, a novel kernelised normalising flow paradigm that integrates kernels into the framework. Our results demonstrate that a kernelised flow can yield competitive or superior results compared to neural network-based flows whilst maintaining parameter efficiency. Kernelised flows excel especially in the low-data regime, enabling flexible non-parametric density estimation in applications with sparse data availability.

The goal of single-channel source separation is to reconstruct K sources given their mixture. In supervised settings where vast amounts of clean source data are available, this challenging, ill-posed problem has been addressed successfully by generative diffusion and flow-based prior models. However, access to such clean source samples is often limited, and even when available, supervised models are vulnerable to domain shifts. To bridge this gap, we present Separation via Unsupervised Remixing Flow (SURF), an unsupervised flow matching approach for source separation that learns directly from observed mixtures. This method relies on a novel combination of state-of-the-art supervised flow matching and regression-based self-supervised techniques. At a high level, starting from a teacher model, we utilize a "remixing" step to bootstrap the learning of a student flow model from the teacher's estimates. We provide insights into the objectives optimized by this approach and draw a novel connection to the Wake-Sleep algorithm. Empirical evaluations on image and audio benchmarks demonstrate that SURF establishes a new state-of-the-art, significantly outperforming existing unsupervised methods. See our demo page for examples. https://google.github.io/df-conformer/surf/

We introduce a one-step generative policy for offline reinforcement learning that maps noise directly to actions via a residual reformulation of MeanFlow, making it compatible with Q-learning. While one-step Gaussian policies enable fast inference, they struggle to capture complex, multimodal action distributions. Existing flow-based methods improve expressivity but typically rely on distillation and two-stage training when trained with Q-learning. To overcome these limitations, we propose to reformulate MeanFlow to enable direct noise-to-action generation by integrating the velocity field and noise-to-action transformation into a single policy network-eliminating the need for separate velocity estimation. We explore several reformulation variants and identify an effective residual formulation that supports expressive and stable policy learning. Our method offers three key advantages: 1) efficient one-step noise-to-action generation, 2) expressive modelling of multimodal action distributions, and 3) efficient and stable policy learning via Q-learning in a single-stage training setup. Extensive experiments on 73 tasks across the OGBench and D4RL benchmarks demonstrate that our method achieves strong performance in both offline and offline-to-online reinforcement learning settings. Code is available at https://github.com/HiccupRL/MeanFlowQL.

Classifier-free guidance is a key component for enhancing the performance of conditional generative models across diverse tasks. While it has previously demonstrated remarkable improvements for the sample quality, it has only been exclusively employed for diffusion models. In this paper, we integrate classifier-free guidance into Flow Matching (FM) models, an alternative simulation-free approach that trains Continuous Normalizing Flows (CNFs) based on regressing vector fields. We explore the usage of Guided Flows for a variety of downstream applications. We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text-to-speech synthesis, boasting state-of-the-art performance. Notably, we are the first to apply flow models for plan generation in the offline reinforcement learning setting, showcasing a 10x speedup in computation compared to diffusion models while maintaining comparable performance.

Transductive few-shot learning has recently triggered wide attention in computer vision. Yet, current methods introduce key hyper-parameters, which control the prediction statistics of the test batches, such as the level of class balance, affecting performances significantly. Such hyper-parameters are empirically grid-searched over validation data, and their configurations may vary substantially with the target dataset and pre-training model, making such empirical searches both sub-optimal and computationally intractable. In this work, we advocate and introduce the unrolling paradigm, also referred to as "learning to optimize", in the context of few-shot learning, thereby learning efficiently and effectively a set of optimized hyper-parameters. Specifically, we unroll a generalization of the ubiquitous Expectation-Maximization (EM) optimizer into a neural network architecture, mapping each of its iterates to a layer and learning a set of key hyper-parameters over validation data. Our unrolling approach covers various statistical feature distributions and pre-training paradigms, including recent foundational vision-language models and standard vision-only classifiers. We report comprehensive experiments, which cover a breadth of fine-grained downstream image classification tasks, showing significant gains brought by the proposed unrolled EM algorithm over iterative variants. The achieved improvements reach up to 10% and 7.5% on vision-only and vision-language benchmarks, respectively.

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new samples from this space. This characteristic creates an intrinsic synergy between representation learning and data generation. However, the generative quality of standard NFs is limited by poor semantic representations from log-likelihood optimization. To remedy this, we propose a novel alignment strategy that creatively leverages the invertibility of NFs: instead of regularizing the forward pass, we align the intermediate features of the generative (reverse) pass with representations from a powerful vision foundation model, demonstrating superior effectiveness over naive alignment. We also introduce a novel training-free, test-time optimization algorithm for classification, which provides a more intrinsic evaluation of the NF's embedded semantic knowledge. Comprehensive experiments demonstrate that our approach accelerates the training of NFs by over 3.3times, while simultaneously delivering significant improvements in both generative quality and classification accuracy. New state-of-the-art results for NFs are established on ImageNet 64times64 and 256times256. Our code is available at https://github.com/MCG-NJU/FlowBack.

In this work, we show that the impact of model capacity varies across timesteps: it is crucial for the early and late stages but largely negligible during the intermediate stage. Accordingly, we propose FlowBlending, a stage-aware multi-model sampling strategy that employs a large model and a small model at capacity-sensitive stages and intermediate stages, respectively. We further introduce simple criteria to choose stage boundaries and provide a velocity-divergence analysis as an effective proxy for identifying capacity-sensitive regions. Across LTX-Video (2B/13B) and WAN 2.1 (1.3B/14B), FlowBlending achieves up to 1.65x faster inference with 57.35% fewer FLOPs, while maintaining the visual fidelity, temporal coherence, and semantic alignment of the large models. FlowBlending is also compatible with existing sampling-acceleration techniques, enabling up to 2x additional speedup. Project page is available at: https://jibin86.github.io/flowblending_project_page.

Flow-based text-to-image (T2I) models excel at prompt-driven image generation, but falter on Image Restoration (IR), often "drifting away" from being faithful to the measurement. Prior work mitigate this drift with data-specific flows or task-specific adapters that are computationally heavy and not scalable across tasks. This raises the question "Can't we efficiently manipulate the existing generative capabilities of a flow model?" To this end, we introduce FlowSteer (FS), an operator-aware conditioning scheme that injects measurement priors along the sampling path,coupling a frozed flow's implicit guidance with explicit measurement constraints. Across super-resolution, deblurring, denoising, and colorization, FS improves measurement consistency and identity preservation in a strictly zero-shot setting-no retrained models, no adapters. We show how the nature of flow models and their sensitivities to noise inform the design of such a scheduler. FlowSteer, although simple, achieves a higher fidelity of reconstructed images, while leveraging the rich generative priors of flow models. All data and code will be publicly available https://tharindu-nirmal.github.io/FlowSteer/{in this link}.

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of high curvature, as shown by previous work, is independence between the source distribution (standard Gaussian) and the data distribution. In this work, we tackle this limitation by two complementary contributions. First, we attempt to break away from the standard Gaussian assumption by introducing κ-FC, a general formulation that conditions the source distribution on an arbitrary signal κ that aligns it better with the data distribution. Then, we present MixFlow, a simple but effective training strategy that reduces the generative path curvatures and considerably improves sampling efficiency. MixFlow trains a flow model on linear mixtures of a fixed unconditional distribution and a κ-FC-based distribution. This simple mixture improves the alignment between the source and data, provides better generation quality with less required sampling steps, and accelerates the training convergence considerably. On average, our training procedure improves the generation quality by 12\% in FID compared to standard rectified flow and 7\% compared to previous baselines under a fixed sampling budget. Code available at: https://github.com/NazirNayal8/MixFlow{https://github.com/NazirNayal8/MixFlow}

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density using a "Russian roulette" estimator, and reduce the memory required during training by using an alternative infinite series for the gradient. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid derivative saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

The nonlinear rheology of a soft glassy material is captured by its constitutive relation, shear stress vs shear rate, which is most generally obtained by sweeping up or down the shear rate over a finite temporal window. For a huge amount of complex fluids, the up and down sweeps do not superimpose and define a rheological hysteresis loop. By means of extensive rheometry coupled to time-resolved velocimetry, we unravel the local scenario involved in rheological hysteresis for various types of well-studied soft materials. We introduce two observables that quantify the hysteresis in macroscopic rheology and local velocimetry respectively, as a function of the sweep rate δt^{-1}. Strikingly, both observables present a robust maximum with δt, which defines a single material-dependent timescale that grows continuously from vanishingly small values in simple yield stress fluids to large values for strongly time-dependent materials. In line with recent theoretical arguments, these experimental results hint at a universal timescale-based framework for soft glassy materials, where inhomogeneous flows characterized by shear bands and/or pluglike flow play a central role.

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

Autoregressive models accumulate error over long rollouts, yet at deployment there is no ground truth to measure it against. We train a single conditional latent diffusion model that steps a dynamical system forward or backward in time via a direction flag, and show that this bidirectionality supplies a measurement-free test-time error signal: rolling forward i steps and then backward i steps must return the model to its start, so the round-trip discrepancy C_i is a self-supervised proxy for the unobservable rollout error: no ensembles, no held-out data, no governing equations, for one extra rollout. We validate on compressible magnetohydrodynamics (MHD), an astrophysical turbulent radiative mixing layer, and natural face videos (CelebV-HQ). On held-out MHD trajectories, C_i ranks rollout error (Spearman 0.91-0.98 at fixed depth; 0.69 pm 0.16 within trajectories), and a simple calibrator fit on training rollouts predicts its magnitude to within 1.14times (68%) and 1.29times (95%) with near-nominal coverage - one nat beyond a depth-only predictor, transferring to all six decoded physical fields. The same signal flags the out-of-distribution Orszag-Tang vortex (AUROC 0.98; 1.0 by depth 10) exactly where sampling-dispersion baselines invert, and it cuts incurred error by 15% at 80% coverage - three times the depth-only baseline. Bidirectional training comes at negative cost, beating direction specialists in both directions, and the backward direction doubles as a fast inverse solver. On LE-PDE-UQ's turbulent Navier-Stokes benchmark, a single bidirectional model reaches accuracy within 1.3times of their ten-model ensemble at a tenth of the training cost, with the best training-free pixel-level calibration. Round-trip consistency turns reversibility into a practical trust signal for generative models.

Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation remains largely unexplored. In this paper, we propose a novel 2D simulation that captures high-dimensional geometric properties in an interpretable 2D setting, enabling us to analyze the learning dynamics of flow matching during training. Based on this analysis, we derive several key insights about flow matching behavior: (1) density approximation can paradoxically degrade performance due to mode discrepancy, (2) directional alignment suffers from path entanglement when overly concentrated, (3) Gaussian's omnidirectional coverage ensures robust learning, and (4) norm misalignment incurs substantial learning costs. Building on these insights, we propose a practical framework that combines norm-aligned training with directionally-pruned sampling. This approach maintains the robust omnidirectional supervision essential for stable flow learning, while eliminating initializations in data-sparse regions during inference. Importantly, our pruning strategy can be applied to any flow matching model trained with a Gaussian source, providing immediate performance gains without the need for retraining. Empirical evaluations demonstrate consistent improvements in both generation quality and sampling efficiency. Our findings provide practical insights and guidelines for source distribution design and introduce a readily applicable technique for improving existing flow matching models. Our code is available at https://github.com/kwanseokk/SourceFM.

Normalizing flows (NFs) provide exact likelihoods and deterministic invertible sampling, but have historically lagged behind diffusion models for large-scale image generation. We identify a key obstacle: NFs are required to learn a single invertible transport over the full ambient space, making them highly sensitive to high-dimensional representations. This leads to a semantic-capacity mismatch in modern visual representation spaces, where semantic information is compact but encoded in overcomplete features. We propose SRC-Flow, which introduces a Semantic Representation Compressor (SRC) to compact high-dimensional RAE features into a low-dimensional semantic space before flow modeling and preserve reconstruction through the frozen RAE decoder. This compact space reduces the modeling burden of NFs and enables effective likelihood-based generation in semantic representation space. We further adopt constant noise regularization tailored to the fixed unconditional bijection learned by flows. On ImageNet 256 times 256 and 512 times 512, SRC-Flow achieves state-of-the-art generation quality among normalizing flow methods, with gFID scores of 1.65 and 2.07 under classifier-free guidance, while retaining exact likelihood computation in the compact semantic representation space and deterministic invertible sampling at the flow level. Codes and models will be available at https://github.com/longtaojiang/SRC-Flow.

River systems operate as inherently interconnected continuous networks, meaning river hydrodynamic simulation ought to be a systemic process. However, widespread hydrology data scarcity often restricts data-driven forecasting to isolated predictions. To achieve systemic simulation and reduce reliance on river observations, we present GraphRiverCast (GRC), a topology-informed AI foundation model designed to simulate multivariate river hydrodynamics in global river systems. GRC is capable of operating in a "ColdStart" mode, generating predictions without relying on historical river states for initialization. In 7-day global pseudo-hindcasts, GRC-ColdStart functions as a robust standalone simulator, achieving a Nash-Sutcliffe Efficiency (NSE) of approximately 0.82 without exhibiting the significant error accumulation typical of autoregressive paradigms. Ablation studies reveal that topological encoding serves as indispensable structural information in the absence of historical states, explicitly guiding hydraulic connectivity and network-scale mass redistribution to reconstruct flow dynamics. Furthermore, when adapted locally via a pre-training and fine-tuning strategy, GRC consistently outperforms physics-based and locally-trained AI baselines. Crucially, this superiority extends from gauged reaches to full river networks, underscoring the necessity of topology encoding and physics-based pre-training. Built on a physics-aligned neural operator architecture, GRC enables rapid and cross-scale adaptive simulation, establishing a collaborative paradigm bridging global hydrodynamic knowledge with local hydrological reality.

Conditional diffusion and flow models routinely fail to satisfy the very constraints that define their task. For instance, a depth-conditioned model often produces images whose re-extracted depth disagrees with the input, even though the forward operator--the depth predictor defining the constraint--is available during both training and inference. Existing approaches generally fall into two categories: supervised models that treat the conditioning signal as a static cue and ignore alignment information at inference, and guidance-based methods that consult it through hand-tuned linear updates, typically trading fidelity to the condition against the plausibility of the generated sample. We argue that the fundamental gap in both paradigms is that the model is never trained to utilize its own alignment error. We introduce FlowBender, a closed-loop framework that treats this error as a first-class input, training the network to learn a correction policy conditioned on inference-time feedback. At each step, an unguided look-ahead pass estimates the clean signal, a task-specific deviation is computed via the forward operator, and a refinement pass consumes this signal to produce a corrected velocity. We propose several variants of FlowBender, including a gradient-based formulation for differentiable operators and a zero-order variant for non-differentiable settings such as JPEG compression. For efficient sampling, we introduce a prior-step shortcut that enables closed-loop correction at a minimal additional computational cost. Across image-to-image translation, restoration, and 3D mesh texturing, FlowBender consistently outperforms standard supervised baselines, alignment-loss-augmented training, and state-of-the-art inference-time guidance, improving fidelity and plausibility simultaneously rather than trading them against each other. Project page: https://flow-bender.github.io/

The multi-step denoising process in diffusion and Flow Matching models causes major efficiency issues, which motivates research on few-step generation. We present Solution Flow Models (SoFlow), a framework for one-step generation from scratch. By analyzing the relationship between the velocity function and the solution function of the velocity ordinary differential equation (ODE), we propose a Flow Matching loss and a solution consistency loss to train our models. The Flow Matching loss allows our models to provide estimated velocity fields for Classifier-Free Guidance (CFG) during training, which improves generation performance. Notably, our consistency loss does not require the calculation of the Jacobian-vector product (JVP), a common requirement in recent works that is not well-optimized in deep learning frameworks like PyTorch. Experimental results indicate that, when trained from scratch using the same Diffusion Transformer (DiT) architecture and an equal number of training epochs, our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.

Using absorbance measurements through a Couette cell containing an emulsion of buoyant droplets, volume fraction profiles are measured at various shear rates. These viscous resuspension experiments allow a direct determination of the normal stress in the vorticity direction in connection with the suspension balance model that has been developed for suspensions of solid particles. The results unambigously show that the normal viscosity responsible for the shear-induced migration of the droplets is independant on the capillary number, implying that particle deformation does not play a great role. It is similar to that of rigid particles at volume fractions below 40\% but much smaller at higher ones.

Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.

Explicitly disentangling style and content in vision models remains challenging due to their semantic overlap and the subjectivity of human perception. Existing methods propose separation through generative or discriminative objectives, but they still face the inherent ambiguity of disentangling intertwined concepts. Instead, we ask: Can we bypass explicit disentanglement by learning to merge style and content invertibly, allowing separation to emerge naturally? We propose SCFlow, a flow-matching framework that learns bidirectional mappings between entangled and disentangled representations. Our approach is built upon three key insights: 1) Training solely to merge style and content, a well-defined task, enables invertible disentanglement without explicit supervision; 2) flow matching bridges on arbitrary distributions, avoiding the restrictive Gaussian priors of diffusion models and normalizing flows; and 3) a synthetic dataset of 510,000 samples (51 styles times 10,000 content samples) was curated to simulate disentanglement through systematic style-content pairing. Beyond controllable generation tasks, we demonstrate that SCFlow generalizes to ImageNet-1k and WikiArt in zero-shot settings and achieves competitive performance, highlighting that disentanglement naturally emerges from the invertible merging process.

Generalist policies can learn a wide range of skills from diverse robot datasets. In order to solve or improve on challenging new tasks, we need a way to infer and invoke the appropriate actions from the policy's rich behavioral prior, especially when directly commanding the policy fails. We focus on flow matching generalists and propose Flow Reversal Steering (FRS): a method that takes suboptimal but ``reasonable'' actions, finds their latent noises by passing them through the flow policy in reverse, and maps them to nearby generalist action modes. We evaluate FRS across many simulated and real-world manipulation settings. First, FRS can turn coarse semantic guidance from humans or vision-language models (VLMs) into corresponding good robot actions, improving zero-shot control. These gains can be distilled with behavioral cloning by training an auxiliary policy to output noises that the generalist maps to good actions -- showing up to 95% absolute task success rate boosts in under a minute of training. Finally, FRS enables policy improvement by bootstrapping reinforcement learning with semantic knowledge, improving on several tasks that standard RL fails to improve on.

Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent work on normalizing flows, ranging from improving their expressive power to expanding their application. We believe the field has now matured and is in need of a unified perspective. In this review, we attempt to provide such a perspective by describing flows through the lens of probabilistic modeling and inference. We place special emphasis on the fundamental principles of flow design, and discuss foundational topics such as expressive power and computational trade-offs. We also broaden the conceptual framing of flows by relating them to more general probability transformations. Lastly, we summarize the use of flows for tasks such as generative modeling, approximate inference, and supervised learning.

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

Unbounded 3D world generation is emerging as a foundational task for scene modeling in computer vision, graphics, and robotics. In this work, we present WorldFlow3D, a novel method capable of generating unbounded 3D worlds. Building upon a foundational property of flow matching - namely, defining a path of transport between two data distributions - we model 3D generation more generally as a problem of flowing through 3D data distributions, not limited to conditional denoising. We find that our latent-free flow approach generates causal and accurate 3D structure, and can use this as an intermediate distribution to guide the generation of more complex structure and high-quality texture - all while converging more rapidly than existing methods. We enable controllability over generated scenes with vectorized scene layout conditions for geometric structure control and visual texture control through scene attributes. We confirm the effectiveness of WorldFlow3D on both real outdoor driving scenes and synthetic indoor scenes, validating cross-domain generalizability and high-quality generation on real data distributions. We confirm favorable scene generation fidelity over approaches in all tested settings for unbounded scene generation. For more, see https://light.princeton.edu/worldflow3d.

Video depth estimation lifts monocular video clips to 3D by inferring dense depth at every frame. Recent advances in single-image depth estimation, brought about by the rise of large foundation models and the use of synthetic training data, have fueled a renewed interest in video depth. However, naively applying a single-image depth estimator to every frame of a video disregards temporal continuity, which not only leads to flickering but may also break when camera motion causes sudden changes in depth range. An obvious and principled solution would be to build on top of video foundation models, but these come with their own limitations; including expensive training and inference, imperfect 3D consistency, and stitching routines for the fixed-length (short) outputs. We take a step back and demonstrate how to turn a single-image latent diffusion model (LDM) into a state-of-the-art video depth estimator. Our model, which we call RollingDepth, has two main ingredients: (i) a multi-frame depth estimator that is derived from a single-image LDM and maps very short video snippets (typically frame triplets) to depth snippets. (ii) a robust, optimization-based registration algorithm that optimally assembles depth snippets sampled at various different frame rates back into a consistent video. RollingDepth is able to efficiently handle long videos with hundreds of frames and delivers more accurate depth videos than both dedicated video depth estimators and high-performing single-frame models. Project page: rollingdepth.github.io.

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models. Our implementation is available at https://github.com/aravindsrinivas/flowpp

Flow matching is a powerful framework for generating high-quality samples in various applications, especially image synthesis. However, the intensive computational demands of these models, especially during the fine-tuning process and sampling processes, pose significant challenges for low-resource scenarios. This paper introduces Bellman Optimal Step-size Straightening (BOSS) technique for distilling flow-matching generative models: it aims specifically for a few-step efficient image sampling while adhering to a computational budget constraint. First, this technique involves a dynamic programming algorithm that optimizes the step sizes of the pretrained network. Then, it refines the velocity network to match the optimal step sizes, aiming to straighten the generation paths. Extensive experimental evaluations across image generation tasks demonstrate the efficacy of BOSS in terms of both resource utilization and image quality. Our results reveal that BOSS achieves substantial gains in efficiency while maintaining competitive sample quality, effectively bridging the gap between low-resource constraints and the demanding requirements of flow-matching generative models. Our paper also fortifies the responsible development of artificial intelligence, offering a more sustainable generative model that reduces computational costs and environmental footprints. Our code can be found at https://github.com/nguyenngocbaocmt02/BOSS.

Large language models have been widely applied, but can inadvertently encode sensitive or harmful information, raising significant safety concerns. Machine unlearning has emerged to alleviate this concern; however, existing training-time unlearning approaches, relying on coarse-grained loss combinations, have limitations in precisely separating knowledge and balancing removal effectiveness with model utility. In contrast, we propose Fine-grained Activation manipuLation by Contrastive Orthogonal uNalignment (FALCON), a novel representation-guided unlearning approach that leverages information-theoretic guidance for efficient parameter selection, employs contrastive mechanisms to enhance representation separation, and projects conflict gradients onto orthogonal subspaces to resolve conflicts between forgetting and retention objectives. Extensive experiments demonstrate that FALCON achieves superior unlearning effectiveness while maintaining model utility, exhibiting robust resistance against knowledge recovery attempts.

Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to improve inference-time efficiency by learning the solution operator of this differential equation. Yet despite their promise, these models lack a unified description that clearly explains how to learn them efficiently in practice. Here, building on the methodology proposed in Boffi et. al. (2024), we present a systematic algorithmic framework for directly learning the flow map associated with a flow or diffusion model. By exploiting a relationship between the velocity field underlying a continuous-time flow and the instantaneous rate of change of the flow map, we show how to convert any distillation scheme into a direct training algorithm via self-distillation, eliminating the need for pre-trained teachers. We introduce three algorithmic families based on different mathematical characterizations of the flow map: Eulerian, Lagrangian, and Progressive methods, which we show encompass and extend all known distillation and direct training schemes for consistency models. We find that the novel class of Lagrangian methods, which avoid both spatial derivatives and bootstrapping from small steps by design, achieve significantly more stable training and higher performance than more standard Eulerian and Progressive schemes. Our methodology unifies existing training schemes under a single common framework and reveals new design principles for accelerated generative modeling. Associated code is available at https://github.com/nmboffi/flow-maps.

Most computer vision systems assume distortion-free images as inputs. The widely used rolling-shutter (RS) image sensors, however, suffer from geometric distortion when the camera and object undergo motion during capture. Extensive researches have been conducted on correcting RS distortions. However, most of the existing work relies heavily on the prior assumptions of scenes or motions. Besides, the motion estimation steps are either oversimplified or computationally inefficient due to the heavy flow warping, limiting their applicability. In this paper, we investigate using rolling shutter with a global reset feature (RSGR) to restore clean global shutter (GS) videos. This feature enables us to turn the rectification problem into a deblur-like one, getting rid of inaccurate and costly explicit motion estimation. First, we build an optic system that captures paired RSGR/GS videos. Second, we develop a novel algorithm incorporating spatial and temporal designs to correct the spatial-varying RSGR distortion. Third, we demonstrate that existing image-to-image translation algorithms can recover clean GS videos from distorted RSGR inputs, yet our algorithm achieves the best performance with the specific designs. Our rendered results are not only visually appealing but also beneficial to downstream tasks. Compared to the state-of-the-art RS solution, our RSGR solution is superior in both effectiveness and efficiency. Considering it is easy to realize without changing the hardware, we believe our RSGR solution can potentially replace the RS solution in taking distortion-free videos with low noise and low budget.

Rectified flow models have become a de facto standard in image generation due to their stable sampling trajectories and high-fidelity outputs. Despite their strong generative capabilities, they face critical limitations in image editing tasks: inaccurate inversion processes for mapping real images back into the latent space, and gradient entanglement issues during editing often result in outputs that do not faithfully reflect the target prompt. Recent efforts have attempted to directly map source and target distributions via ODE-based approaches without inversion; however,these methods still yield suboptimal editing quality. In this work, we propose a flow decomposition-and-aggregation framework built upon an inversion-free formulation to address these limitations. Specifically, we semantically decompose the target prompt into multiple sub-prompts, compute an independent flow for each, and aggregate them to form a unified editing trajectory. While we empirically observe that decomposing the original flow enhances diversity in the target space, generating semantically aligned outputs still requires consistent guidance toward the full target prompt. To this end, we design a projection and soft-aggregation mechanism for flow, inspired by gradient conflict resolution in multi-task learning. This approach adaptively weights the sub-target velocity fields, suppressing semantic redundancy while emphasizing distinct directions, thereby preserving both diversity and consistency in the final edited output. Experimental results demonstrate that our method outperforms existing zero-shot editing approaches in terms of semantic fidelity and attribute disentanglement. The code is available at https://github.com/Harvard-AI-and-Robotics-Lab/SplitFlow.

Given an unconditional generative model and a predictor for a target property (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. As a highly efficient technique for steering generative models toward flexible outcomes, training-free guidance has gained increasing attention in diffusion models. However, existing methods only handle data in continuous spaces, while many scientific applications involve both continuous and discrete data (referred to as multimodality). Another emerging trend is the growing use of the simple and general flow matching framework in building generative foundation models, where guided generation remains under-explored. To address this, we introduce TFG-Flow, a novel training-free guidance method for multimodal generative flow. TFG-Flow addresses the curse-of-dimensionality while maintaining the property of unbiased sampling in guiding discrete variables. We validate TFG-Flow on four molecular design tasks and show that TFG-Flow has great potential in drug design by generating molecules with desired properties.

A common recipe to improve diffusion models at test-time so that samples score highly against a user-specified reward is to introduce the gradient of the reward into the dynamics of the diffusion itself. This procedure is often ill posed, as user-specified rewards are usually only well defined on the data distribution at the end of generation. While common workarounds to this problem are to use a denoiser to estimate what a sample would have been at the end of generation, we propose a simple solution to this problem by working directly with a flow map. By exploiting a relationship between the flow map and velocity field governing the instantaneous transport, we construct an algorithm, Flow Map Trajectory Tilting (FMTT), which provably performs better ascent on the reward than standard test-time methods involving the gradient of the reward. The approach can be used to either perform exact sampling via importance weighting or principled search that identifies local maximizers of the reward-tilted distribution. We demonstrate the efficacy of our approach against other look-ahead techniques, and show how the flow map enables engagement with complicated reward functions that make possible new forms of image editing, e.g. by interfacing with vision language models.

We study the dynamics of Stochastic Gradient Descent (SGD), which is known to steer deep neural networks toward invariant sets that correspond to simpler subnetworks. How this steering unfolds over time remains poorly understood. We answer this by modeling the stochastic gradient flow (SGF) as a percolation process, in which architectural symmetries force subnetworks to merge in discrete simultaneous blocks rather than one at a time. These structural transitions register as variance spikes in a macroscopic order parameter, echoing physical phase transitions. We further show this trapping mechanism and its associated scaling cascade extend to Adam and AdamW under an explicit heavy-tailed noise model.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

Accurately predicting the future fluid is important to extensive areas, such as meteorology, oceanology and aerodynamics. However, since the fluid is usually observed from an Eulerian perspective, its active and intricate dynamics are seriously obscured and confounded in static grids, bringing horny challenges to the prediction. This paper introduces a new Lagrangian-guided paradigm to tackle the tanglesome fluid dynamics. Instead of solely predicting the future based on Eulerian observations, we propose the Eulerian-Lagrangian Dual Recurrent Network (EuLagNet), which captures multiscale fluid dynamics by tracking movements of adaptively sampled key particles on multiple scales and integrating dynamics information over time. Concretely, a EuLag Block is presented to communicate the learned Eulerian and Lagrangian features at each moment and scale, where the motion of tracked particles is inferred from Eulerian observations and their accumulated dynamics information is incorporated into Eulerian fields to guide future prediction. Tracking key particles not only provides a clear and interpretable clue for fluid dynamics but also makes our model free from modeling complex correlations among massive grids for better efficiency. Experimentally, EuLagNet excels in three challenging fluid prediction tasks, covering both 2D and 3D, simulated and real-world fluids.

The grand vision of enabling persistent, large-scale 3D visual geometry understanding is shackled by the irreconcilable demands of scalability and long-term stability. While offline models like VGGT achieve inspiring geometry capability, their batch-based nature renders them irrelevant for live systems. Streaming architectures, though the intended solution for live operation, have proven inadequate. Existing methods either fail to support truly infinite-horizon inputs or suffer from catastrophic drift over long sequences. We shatter this long-standing dilemma with InfiniteVGGT, a causal visual geometry transformer that operationalizes the concept of a rolling memory through a bounded yet adaptive and perpetually expressive KV cache. Capitalizing on this, we devise a training-free, attention-agnostic pruning strategy that intelligently discards obsolete information, effectively ``rolling'' the memory forward with each new frame. Fully compatible with FlashAttention, InfiniteVGGT finally alleviates the compromise, enabling infinite-horizon streaming while outperforming existing streaming methods in long-term stability. The ultimate test for such a system is its performance over a truly infinite horizon, a capability that has been impossible to rigorously validate due to the lack of extremely long-term, continuous benchmarks. To address this critical gap, we introduce the Long3D benchmark, which, for the first time, enables a rigorous evaluation of continuous 3D geometry estimation on sequences about 10,000 frames. This provides the definitive evaluation platform for future research in long-term 3D geometry understanding. Code is available at: https://github.com/AutoLab-SAI-SJTU/InfiniteVGGT

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are considered: 1. interpretability of machine-learned results, 2. bulking out of training data, and 3. generalizability of neural networks. For the interpretability, we first demonstrate two methods to observe the internal procedure of neural networks, i.e., visualization of hidden layers and application of gradient-weighted class activation mapping (Grad-CAM), applied to canonical fluid flow estimation problems -- (1) drag coefficient estimation of a cylinder wake and (2) velocity estimation from particle images. It is exemplified that both approaches can successfully tell us evidences of the great capability of machine learning-based estimations. We then utilize some techniques to bulk out training data for super-resolution analysis and temporal prediction for cylinder wake and NOAA sea surface temperature data to demonstrate that sufficient training of neural networks with limited amount of training data can be achieved for fluid flow problems. The generalizability of machine learning model is also discussed by accounting for the perspectives of inter/extrapolation of training data, considering super-resolution of wakes behind two parallel cylinders. We find that various flow patterns generated by complex interaction between two cylinders can be reconstructed well, even for the test configurations regarding the distance factor. The present paper can be a significant step toward practical uses of neural networks for both laminar and turbulent flow problems.

We propose Flow-Anchored Noise-conditioned Q-Learning (FAN), a highly efficient and high-performing offline reinforcement learning (RL) algorithm. Recent work has shown that expressive flow policies and distributional critics improve offline RL performance, but at a high computational cost. Specifically, flow policies require iterative sampling to produce a single action, and distributional critics require computation over multiple samples (e.g., quantiles) to estimate value. To address these inefficiencies while maintaining high performance, we introduce FAN. Our method employs a behavior regularization technique that utilizes only a single flow policy iteration and requires only a single Gaussian noise sample for distributional critics. Our theoretical analysis of convergence and performance bounds demonstrates that these simplifications not only improve efficiency but also lead to superior task performance. Experiments on robotic manipulation and locomotion tasks demonstrate that FAN achieves state-of-the-art performance while significantly reducing both training and inference runtimes. We release our code at https://github.com/brianlsy98/FAN.

MeanFlow has recently emerged as a powerful framework for few-step generative modeling trained from scratch, but its success is not yet fully understood. In this work, we show that the MeanFlow objective naturally decomposes into two parts: trajectory flow matching and trajectory consistency. Through gradient analysis, we find that these terms are strongly negatively correlated, causing optimization conflict and slow convergence. Motivated by these insights, we introduce alpha-Flow, a broad family of objectives that unifies trajectory flow matching, Shortcut Model, and MeanFlow under one formulation. By adopting a curriculum strategy that smoothly anneals from trajectory flow matching to MeanFlow, alpha-Flow disentangles the conflicting objectives, and achieves better convergence. When trained from scratch on class-conditional ImageNet-1K 256x256 with vanilla DiT backbones, alpha-Flow consistently outperforms MeanFlow across scales and settings. Our largest alpha-Flow-XL/2+ model achieves new state-of-the-art results using vanilla DiT backbones, with FID scores of 2.58 (1-NFE) and 2.15 (2-NFE).

With the success of flow matching in visual generation, sampling efficiency remains a critical bottleneck for its practical application. Among flow models' accelerating methods, ReFlow has been somehow overlooked although it has theoretical consistency with flow matching. This is primarily due to its suboptimal performance in practical scenarios compared to consistency distillation and score distillation. In this work, we investigate this issue within the ReFlow framework and propose FlowSteer, a method unlocks the potential of ReFlow-based distillation by guiding the student along teacher's authentic generation trajectories. We first identify that Piecewised ReFlow's performance is hampered by a critical distribution mismatch during the training and propose Online Trajectory Alignment(OTA) to resolve it. Then, we introduce a adversarial distillation objective applied directly on the ODE trajectory, improving the student's adherence to the teacher's generation trajectory. Furthermore, we find and fix a previously undiscovered flaw in the widely-used FlowMatchEulerDiscreteScheduler that largely degrades few-step inference quality. Our experiment result on SD3 demonstrates our method's efficacy.

Large-scale generative models have shown impressive image-generation capabilities, propelled by massive data. However, this often inadvertently leads to the generation of harmful or inappropriate content and raises copyright concerns. Driven by these concerns, machine unlearning has become crucial to effectively purge undesirable knowledge from models. While existing literature has studied various unlearning techniques, these often suffer from either poor unlearning quality or degradation in text-image alignment after unlearning, due to the competitive nature of these objectives. To address these challenges, we propose a framework that seeks an optimal model update at each unlearning iteration, ensuring monotonic improvement on both objectives. We further derive the characterization of such an update. In addition, we design procedures to strategically diversify the unlearning and remaining datasets to boost performance improvement. Our evaluation demonstrates that our method effectively removes target classes from recent diffusion-based generative models and concepts from stable diffusion models while maintaining close alignment with the models' original trained states, thus outperforming state-of-the-art baselines. Our code will be made available at https://github.com/reds-lab/Restricted_gradient_diversity_unlearning.git.

Large language model (LLM) unlearning has become a critical mechanism for removing undesired data, knowledge, or behaviors from pre-trained models while retaining their general utility. Yet, with the rise of open-weight LLMs, we ask: can the unlearning process itself be backdoored, appearing successful under normal conditions yet reverting to pre-unlearned behavior when a hidden trigger is activated? Drawing inspiration from classical backdoor attacks that embed triggers into training data to enforce specific behaviors, we investigate backdoor unlearning, where models forget as intended in the clean setting but recover forgotten knowledge when the trigger appears. We show that designing such attacks presents unique challenges, hinging on where triggers are placed and how backdoor training is reinforced. We uncover a strong link between backdoor efficacy and the attention sink phenomenon, i.e., shallow input tokens consistently attract disproportionate attention in LLMs. Our analysis reveals that these attention sinks serve as gateways for backdoor unlearning: placing triggers at sink positions and aligning their attention values markedly enhances backdoor persistence. Extensive experiments validate these findings, showing that attention-sink-guided backdoor unlearning reliably restores forgotten knowledge in the presence of backdoor triggers, while behaving indistinguishably from a normally unlearned model when triggers are absent. Code is available at https://github.com/OPTML-Group/Unlearn-Backdoor.

We present an online reinforcement learning (RL) algorithm for fine-tuning flow-matching policies in continuous-control problems. Our key insight is to view RL-based policy improvement as a transport of action densities towards regions of high reward, which naturally aligns with the transport formulation of flow matching models. Prior methods either approximate the current or optimal policy distribution or resort to distillation, which introduces biased gradients or sacrifices multimodal modeling capacity. In contrast, our approach for RL with Density Transport, which we name RLDT, constructs a transport field from a maximum-entropy RL objective using Stein Variational Gradient Descent (SVGD). Then, it finetunes a pretrained flow matching policy to align with this field. Training with this alignment objective is nontrivial because flow-matching policies generate actions via a multi-step process, making direct gradient-based optimization challenging. To overcome this challenge and stabilize training, we approximate policy actions from intermediate denoising steps via expected-target estimation. This allows the transport-field update to propagate into the network parameters without unstable backpropagation through time. Experimental results demonstrate that RLDT outperforms competitive baselines in reward quality and convergence speed. This performance holds across diverse continuous-control tasks, encompassing both dense and sparse rewards, as well as state- and vision-based long-horizon robot manipulation. The project webpage is https://rpfey.github.io/rldt/{https://rpfey.github.io/rldt/}.

In this paper, we introduce agentic unlearning which removes specified information from both model parameters and persistent memory in agents with closed-loop interaction. Existing unlearning methods target parameters alone, leaving two critical gaps: (i) parameter-memory backflow, where retrieval reactivates parametric remnants or memory artifacts reintroduce sensitive content, and (ii) the absence of a unified strategy that covers both parameter and memory pathways. We present Synchronized Backflow Unlearning (SBU), a framework that unlearns jointly across parameter and memory pathways. The memory pathway performs dependency closure-based unlearning that prunes isolated entities while logically invalidating shared artifacts. The parameter pathway employs stochastic reference alignment to guide model outputs toward a high-entropy prior. These pathways are integrated via a synchronized dual-update protocol, forming a closed-loop mechanism where memory unlearning and parametric suppression reinforce each other to prevent cross-pathway recontamination. Experiments on medical QA benchmarks show that SBU reduces traces of targeted private information across both pathways with limited degradation on retained data.

Information on liquid jet stream flow is crucial in many real world applications. In a large number of cases, these flows fall directly onto free surfaces (e.g. pools), creating a splash with accompanying splashing sounds. The sound produced is supplied by energy interactions between the liquid jet stream and the passive free surface. In this investigation, we collect the sound of a water jet of varying flowrate falling into a pool of water, and use this sound to predict the flowrate and flowrate trajectory involved. Two approaches are employed: one uses machine-learning models trained using audio features extracted from the collected sound to predict the flowrate (and subsequently the flowrate trajectory). In contrast, the second method directly uses acoustic parameters related to the spectral energy of the liquid-liquid interaction to estimate the flowrate trajectory. The actual flowrate, however, is determined directly using a gravimetric method: tracking the change in mass of the pooling liquid over time. We show here that the two methods agree well with the actual flowrate and offer comparable performance in accurately predicting the flowrate trajectory, and accordingly offer insights for potential real-life applications using sound.

Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how fluids interact with genuinely novel surfaces not seen during training. We introduce SURFSUP, a framework that represents objects implicitly using signed distance functions (SDFs), rather than an explicit representation of meshes or particles. This continuous representation of geometry enables more accurate simulation of fluid-object interactions over long time periods while simultaneously making computation more efficient. Moreover, SURFSUP trained on simple shape primitives generalizes considerably out-of-distribution, even to complex real-world scenes and objects. Finally, we show we can invert our model to design simple objects to manipulate fluid flow.

Large language models (LLMs) have shown to pose social and ethical risks such as generating toxic language or facilitating malicious use of hazardous knowledge. Machine unlearning is a promising approach to improve LLM safety by directly removing harmful behaviors and knowledge. In this paper, we propose "SPlit, UNlearn, MerGE" (SPUNGE), a framework that can be used with any unlearning method to amplify its effectiveness. SPUNGE leverages data attributes during unlearning by splitting unlearning data into subsets based on specific attribute values, unlearning each subset separately, and merging the unlearned models. We empirically demonstrate that SPUNGE significantly improves the performance of two recent unlearning methods on state-of-the-art LLMs while maintaining their general capabilities on standard academic benchmarks.

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling the random numbers of the next model in the stack, we obtain a type of normalizing flow suitable for density estimation, which we call Masked Autoregressive Flow. This type of flow is closely related to Inverse Autoregressive Flow and is a generalization of Real NVP. Masked Autoregressive Flow achieves state-of-the-art performance in a range of general-purpose density estimation tasks.

Recent advances in flow-based generative models have enabled training-free, text-guided image editing by inverting an image into its latent noise and regenerating it under a new target conditional guidance. However, existing methods struggle to preserve source fidelity: higher-order solvers incur additional model inferences, truncated inversion constrains editability, and feature injection methods lack architectural transferability. To address these limitations, we propose SteerFlow, a model-agnostic editing framework with strong theoretical guarantees on source fidelity. In the forward process, we introduce an Amortized Fixed-Point Solver that implicitly straightens the forward trajectory by enforcing velocity consistency across consecutive timesteps, yielding a high-fidelity inverted latent. In the backward process, we introduce Trajectory Interpolation, which adaptively blends target-editing and source-reconstruction velocities to keep the editing trajectory anchored to the source. To further improve background preservation, we introduce an Adaptive Masking mechanism that spatially constrains the editing signal with concept-guided segmentation and source-target velocity differences. Extensive experiments on FLUX.1-dev and Stable Diffusion 3.5 Medium demonstrate that SteerFlow consistently achieves better editing quality than existing methods. Finally, we show that SteerFlow extends naturally to a complex multi-turn editing paradigm without accumulating drift.

With the prosper of video diffusion models, down-stream applications like video editing have been significantly promoted without consuming much computational cost. One particular challenge in this task lies at the motion transfer process from the source video to the edited one, where it requires the consideration of the shape deformation in between, meanwhile maintaining the temporal consistency in the generated video sequence. However, existing methods fail to model complicated motion patterns for video editing, and are fundamentally limited to object replacement, where tasks with non-rigid object motions like multi-object and portrait editing are largely neglected. In this paper, we observe that optical flows offer a promising alternative in complex motion modeling, and present FlowV2V to re-investigate video editing as a task of flow-driven Image-to-Video (I2V) generation. Specifically, FlowV2V decomposes the entire pipeline into first-frame editing and conditional I2V generation, and simulates pseudo flow sequence that aligns with the deformed shape, thus ensuring the consistency during editing. Experimental results on DAVIS-EDIT with improvements of 13.67% and 50.66% on DOVER and warping error illustrate the superior temporal consistency and sample quality of FlowV2V compared to existing state-of-the-art ones. Furthermore, we conduct comprehensive ablation studies to analyze the internal functionalities of the first-frame paradigm and flow alignment in the proposed method.

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for training CNFs based on regressing vector fields of fixed conditional probability paths. Flow Matching is compatible with a general family of Gaussian probability paths for transforming between noise and data samples -- which subsumes existing diffusion paths as specific instances. Interestingly, we find that employing FM with diffusion paths results in a more robust and stable alternative for training diffusion models. Furthermore, Flow Matching opens the door to training CNFs with other, non-diffusion probability paths. An instance of particular interest is using Optimal Transport (OT) displacement interpolation to define the conditional probability paths. These paths are more efficient than diffusion paths, provide faster training and sampling, and result in better generalization. Training CNFs using Flow Matching on ImageNet leads to consistently better performance than alternative diffusion-based methods in terms of both likelihood and sample quality, and allows fast and reliable sample generation using off-the-shelf numerical ODE solvers.

Activation steering has emerged as a promising alternative for controlling language-model behavior at inference time by modifying intermediate representations while keeping model parameters frozen. However, large-scale evaluations such as AxBench show that existing steering methods are often outperformed by simple in-context prompting and generalize poorly to unseen concepts. We hypothesize that these limitations arise from unvalidated simplifying assumptions shared across prior methods, which typically restrict steering interventions to fixed, single-step, position-invariant transforms. We propose FLAS (Flow-based Activation Steering), which learns a general, concept-conditioned velocity field v_t(h,t,c) that transports unsteered activations to steered ones without relying on these assumptions. On AxBench, FLAS is the first learned method to consistently outperform prompting, reaching held-out harmonic means of 1.015 on Gemma-2-2B-IT and 1.113 on Gemma-2-9B-IT without per-concept tuning. Analysis of the learned flow shows curved, multi-step, token-varying trajectories, which suggests that previous hypotheses on activation space geometry might be incomplete.

Machine Unlearning is rising as a new field, driven by the pressing necessity of ensuring privacy in modern artificial intelligence models. This technique primarily aims to eradicate any residual influence of a specific subset of data from the knowledge acquired by a neural model during its training. This work introduces a novel unlearning algorithm, denoted as Distance-based Unlearning via Centroid Kinematics (DUCK), which employs metric learning to guide the removal of samples matching the nearest incorrect centroid in the embedding space. Evaluation of the algorithm's performance is conducted across various benchmark datasets in two distinct scenarios, class removal, and homogeneous sampling removal, obtaining state-of-the-art performance. We also introduce a novel metric, called Adaptive Unlearning Score (AUS), encompassing not only the efficacy of the unlearning process in forgetting target data but also quantifying the performance loss relative to the original model. Additionally, we conducted a thorough investigation of the unlearning mechanism in DUCK, examining its impact on the organization of the feature space and employing explainable AI techniques for deeper insights.

Moist convection is a physical process where the latent heat released by condensation acts as a buoyancy source that can enhance or even trigger an overturning convective instability. Since the saturation temperature often decreases with height, condensation releases latent heat preferentially in regions of upflow. Due to this inhomogeneous heat source, moist convection may be more sensitive to changes in flow morphology, such as those induced by rotation, than dry Rayleigh-B\'enard convection. In order to study the effects of rotation on flows driven by latent heat release, we present a suite of numerical simulations that solve the Rainy-B\'enard equations (Vallis et al. 2019). We identify three morphological regimes: a cellular regime and a plume regime broadly analogous to those found in rotating Rayleigh B\'enard convection, and a novel funnel regime that lacks a clear analog within the regimes exhibited by dry convection. We measure energy fluxes through the system and report rotational scalings of the Reynolds and moist Nusselt numbers. We find that moist static energy transport, as measured by a moist Nusselt number, is significantly enhanced in the funnel regime without a corresponding enhancement in Reynolds number, indicating that this funnel regime produces structures with more favorable correlations between the temperature and vertical velocity.

Large language models (LLMs) may memorize sensitive or copyrighted content, raising privacy and legal concerns. Due to the high cost of retraining from scratch, researchers attempt to employ machine unlearning to remove specific content from LLMs while preserving the overall performance. In this paper, we discuss several issues in machine unlearning for LLMs and provide our insights on possible approaches. To address the issue of inadequate evaluation of model outputs after unlearning, we introduce three additional metrics to evaluate token diversity, sentence semantics, and factual correctness. We then categorize unlearning methods into untargeted and targeted, and discuss their issues respectively. Specifically, the behavior that untargeted unlearning attempts to approximate is unpredictable and may involve hallucinations, and existing regularization is insufficient for targeted unlearning. To alleviate these issues, we propose using the objective of maximizing entropy (ME) for untargeted unlearning and incorporate answer preservation (AP) loss as regularization for targeted unlearning. Experimental results across three scenarios, i.e., fictitious unlearning, continual unlearning, and real-world unlearning, demonstrate the effectiveness of our approaches. The code is available at https://github.com/sail-sg/closer-look-LLM-unlearning.

Current LLM unlearning methods are not robust. A few steps of finetuning can revert their effects. We begin by showing that this is true even for an idealized form of unlearning: training to imitate a model that was never trained on unwanted information. This shows that training a model can drastically modify its input-output behavior while leaving its underlying capabilities intact. In light of this dynamic, we show our main result. Training a randomly initialized student on the outputs of an unlearned model transfers behaviors while leaving latent capabilities behind. In short, distillation robustifies unlearning. Based on this result, we propose Unlearn-Noise-Distill-on-Outputs (UNDO), a scalable method that distills an unlearned model into a noised copy of itself. UNDO introduces a tunable tradeoff between compute cost and robustness, establishing a new Pareto frontier on synthetic language and arithmetic tasks. At its strongest setting, UNDO matches the robustness of a model retrained from scratch with perfect data filtering while using only 60-80% of the compute and requiring only 0.01% of the pretraining data to be labeled. We also show that UNDO robustifies unlearning on the more realistic Weapons of Mass Destruction Proxy (WMDP) benchmark. Since distillation is widely used in practice, incorporating an unlearning step beforehand offers a convenient path to robust capability removal.

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose Flow Advantage-Weighted Rectification (FlowAWR), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2times to 5times convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in >4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

We present FloodDiffusion, a new framework for text-driven, streaming human motion generation. Given time-varying text prompts, FloodDiffusion generates text-aligned, seamless motion sequences with real-time latency. Unlike existing methods that rely on chunk-by-chunk or auto-regressive model with diffusion head, we adopt a diffusion forcing framework to model this time-series generation task under time-varying control events. We find that a straightforward implementation of vanilla diffusion forcing (as proposed for video models) fails to model real motion distributions. We demonstrate that to guarantee modeling the output distribution, the vanilla diffusion forcing must be tailored to: (i) train with a bi-directional attention instead of casual attention; (ii) implement a lower triangular time scheduler instead of a random one; (iii) utilize a continues time-varying way to introduce text conditioning. With these improvements, we demonstrate in the first time that the diffusion forcing-based framework achieves state-of-the-art performance on the streaming motion generation task, reaching an FID of 0.057 on the HumanML3D benchmark. Models, code, and weights are available. https://shandaai.github.io/FloodDiffusion/

Recent advances in diffusion/flow-matching policies have enabled imitation learning of complex, multi-modal action trajectories. However, they are computationally expensive because they sample a trajectory of trajectories: a diffusion/flow trajectory of action trajectories. They discard intermediate action trajectories, and must wait for the sampling process to complete before any actions can be executed on the robot. We simplify diffusion/flow policies by treating action trajectories as flow trajectories. Instead of starting from pure noise, our algorithm samples from a narrow Gaussian around the last action. Then, it incrementally integrates a velocity field learned via flow matching to produce a sequence of actions that constitute a single trajectory. This enables actions to be streamed to the robot on-the-fly during the flow sampling process, and is well-suited for receding horizon policy execution. Despite streaming, our method retains the ability to model multi-modal behavior. We train flows that stabilize around demonstration trajectories to reduce distribution shift and improve imitation learning performance. Streaming flow policy outperforms prior methods while enabling faster policy execution and tighter sensorimotor loops for learning-based robot control. Project website: https://streaming-flow-policy.github.io/

Numerical analysis of unconfined flow over an obstacle has always been challenging in computational fluid dynamics due to the truncation of the computational domain while replicating the real-life flows and the application of the boundary conditions. Confined flows studies have been well established and documented while unconfined flow studies are relatively challenging. Present work demonstrates the implementation of lattice Boltzmann method for unconfined flow over a circular cylinder for Re 100. The cylinder was placed at 10D upstream and 30D downstream and 10D from both the top and bottom walls. Different boundary conditions were implemented at the top and bottom walls to ensure unconfined flow. Drag and lift coefficients are also presented and were computed using the momentum exchange algorithm. Results are in complete agreement with the existing literature which demonstrate the capability of the solver.

Recent deep learning-based optical flow estimators have exhibited impressive performance in generating local flows between consecutive frames. However, the estimation of long-range flows between distant frames, particularly under complex object deformation and large motion occlusion, remains a challenging task. One promising solution is to accumulate local flows explicitly or implicitly to obtain the desired long-range flow. Nevertheless, the accumulation errors and flow misalignment can hinder the effectiveness of this approach. This paper proposes a novel recurrent framework called AccFlow, which recursively backward accumulates local flows using a deformable module called as AccPlus. In addition, an adaptive blending module is designed along with AccPlus to alleviate the occlusion effect by backward accumulation and rectify the accumulation error. Notably, we demonstrate the superiority of backward accumulation over conventional forward accumulation, which to the best of our knowledge has not been explicitly established before. To train and evaluate the proposed AccFlow, we have constructed a large-scale high-quality dataset named CVO, which provides ground-truth optical flow labels between adjacent and distant frames. Extensive experiments validate the effectiveness of AccFlow in handling long-range optical flow estimation. Codes are available at https://github.com/mulns/AccFlow .

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this error and enable faster sampling. However, their training typically demands architectural changes that limit compatibility with pretrained flow models. We introduce Decoupled MeanFlow, a simple decoding strategy that converts flow models into flow map models without architectural modifications. Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps. Combined with enhanced training techniques, this design enables high-quality generation in as few as 1 to 4 steps. Notably, we find that training flow models and subsequently converting them is more efficient and effective than training flow maps from scratch. On ImageNet 256x256 and 512x512, our models attain 1-step FID of 2.16 and 2.12, respectively, surpassing prior art by a large margin. Furthermore, we achieve FID of 1.51 and 1.68 when increasing the steps to 4, which nearly matches the performance of flow models while delivering over 100x faster inference.

Flow-based generative models have been employed for sampling the Boltzmann distribution, but their application to high-dimensional systems is hindered by the significant computational cost of obtaining the Jacobian of the flow. To overcome this challenge, we introduce the flow perturbation method, which incorporates optimized stochastic perturbations into the flow. By reweighting trajectories generated by the perturbed flow, our method achieves unbiased sampling of the Boltzmann distribution with orders of magnitude speedup compared to both brute force Jacobian calculations and the Hutchinson estimator. Notably, it accurately sampled the Chignolin protein with all atomic Cartesian coordinates explicitly represented, which, to our best knowledge, is the largest molecule ever Boltzmann sampled in such detail using generative models.

Classifier-Free Guidance (CFG) is a widely adopted technique in diffusion/flow models to improve image fidelity and controllability. In this work, we first analytically study the effect of CFG on flow matching models trained on Gaussian mixtures where the ground-truth flow can be derived. We observe that in the early stages of training, when the flow estimation is inaccurate, CFG directs samples toward incorrect trajectories. Building on this observation, we propose CFG-Zero*, an improved CFG with two contributions: (a) optimized scale, where a scalar is optimized to correct for the inaccuracies in the estimated velocity, hence the * in the name; and (b) zero-init, which involves zeroing out the first few steps of the ODE solver. Experiments on both text-to-image (Lumina-Next, Stable Diffusion 3, and Flux) and text-to-video (Wan-2.1) generation demonstrate that CFG-Zero* consistently outperforms CFG, highlighting its effectiveness in guiding Flow Matching models. (Code is available at github.com/WeichenFan/CFG-Zero-star)

On-policy distillation (OPD) trains student models under their own induced distribution while leveraging supervision from stronger teachers. We identify a failure mode of OPD: as training progresses, on-policy rollouts can undergo abrupt length inflation, causing truncated trajectories to dominate the training data. This truncation collapse coincides with abrupt repetition saturation and induces biased gradient signals, leading to severe training instability and sharp degradation in validation performance. We attribute this problem to the interaction between student-induced data collection and the distillation objective, which implicitly favors long and repetitive rollouts. To address this issue, we propose StableOPD, a stabilized OPD framework that combines a reference-based divergence constraint with rollout mixture distillation. These together mitigate repetition-induced length inflation and further stabilize OPD training. Across multiple math reasoning datasets, our approach prevents truncation collapse, stabilizes training dynamics, and improves performance by 7.2% on average.

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the L_2 regularization as an upper bound of the 2-Wasserstein distance (W_2), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the L_2 (or upper bound of W_2) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the parameterization of an easily invertible elementwise transformation, whose choice determines the flexibility of these models. Building upon recent work, we propose a fully-differentiable module based on monotonic rational-quadratic splines, which enhances the flexibility of both coupling and autoregressive transforms while retaining analytic invertibility. We demonstrate that neural spline flows improve density estimation, variational inference, and generative modeling of images.

Text-driven video editing aims to modify video content according to natural language instructions. While recent training-free approaches have made progress by leveraging pre-trained diffusion models, they typically rely on inversion-based techniques that map input videos into the latent space, which often leads to temporal inconsistencies and degraded structural fidelity. To address this, we propose FlowDirector, a novel inversion-free video editing framework. Our framework models the editing process as a direct evolution in data space, guiding the video via an Ordinary Differential Equation (ODE) to smoothly transition along its inherent spatiotemporal manifold, thereby preserving temporal coherence and structural details. To achieve localized and controllable edits, we introduce an attention-guided masking mechanism that modulates the ODE velocity field, preserving non-target regions both spatially and temporally. Furthermore, to address incomplete edits and enhance semantic alignment with editing instructions, we present a guidance-enhanced editing strategy inspired by Classifier-Free Guidance, which leverages differential signals between multiple candidate flows to steer the editing trajectory toward stronger semantic alignment without compromising structural consistency. Extensive experiments across benchmarks demonstrate that FlowDirector achieves state-of-the-art performance in instruction adherence, temporal consistency, and background preservation, establishing a new paradigm for efficient and coherent video editing without inversion.

Interactive video generation and editing are becoming increasingly important for creative design. In this report, we introduce EditStream: a unified framework for interactive video generation and editing. EditStream unifies multiple video creation and manipulation tasks within a single DiT-based model through flexible task-specific conditioning, and further transforms it into a fast, few-step autoregressive model for efficient streaming. It supports Text-to-Video, Image-to-Video, Video-to-Video, Editing Propagation, Reference-guided Video Editing, and Camera Pose Change, enabling flexible control over video generation, transformation, and editing within one system. To make the unified model practical for interactive use, we develop a two-stage distillation approach that combines Velocity Moment Matching (VMM) with autoregressive unrolling. VMM matches conditional velocity moments at student-reached intermediate states to preserve generation quality and motion, while unrolling exposes the student to its own autoregressive predictions to improve temporal stability. Together, they alleviate common challenges in few-step autoregressive video generation, including over-saturation, degraded motion, temporal instability, and complex training. EditStream provides a practical and scalable solution that bridges high-quality diffusion-based video models with interactive creative workflows.

Focusing on simulated dilute polymer solutions, this letter investigates the interactions between flow structures and organized polymer stress sheets for the steady arrowhead coherent structure in a two-dimensional periodic channel flow. Formulating the problem in a frame of reference moving with the arrowhead velocity, streamlines, which are also pathlines in this frame, enables the identification of two distinct topological regions linked to two stagnation points. The streamlines help connecting the spatial distribution of polymer stress within the sheets and the dynamics of polymers transported by the flow. Using stresslines, lines parallel to the eigenvectors of polymer stress, a novel formulation of the viscoelastic stress term in the momentum transport equation proposes a more intuitive interpretation of the relation between the curvature of the stresslines, and the variation of stress along these lines, with the local flow topology. An approximation of this formulation is shown to explain the pressure jump observed in the arrowhead structure as a function of the local curvature of the polymer stress sheet.

Diffusion models are widely used for generative tasks across domains. Given a pre-trained diffusion model, it is often desirable to fine-tune it further either to correct for errors in learning or to align with downstream applications. Towards this, we examine the effect of shaping the distribution at intermediate noise levels induced by diffusion models. First, we show that existing variants of Rejection sAmpling based Fine-Tuning (RAFT), which we unify as GRAFT, can implicitly perform KL regularized reward maximization with reshaped rewards. Motivated by this observation, we introduce P-GRAFT to shape distributions at intermediate noise levels and demonstrate empirically that this can lead to more effective fine-tuning. We mathematically explain this via a bias-variance tradeoff. Next, we look at correcting learning errors in pre-trained flow models based on the developed mathematical framework. In particular, we propose inverse noise correction, a novel algorithm to improve the quality of pre-trained flow models without explicit rewards. We empirically evaluate our methods on text-to-image(T2I) generation, layout generation, molecule generation and unconditional image generation. Notably, our framework, applied to Stable Diffusion v2, improves over policy gradient methods on popular T2I benchmarks in terms of VQAScore and shows an 8.81% relative improvement over the base model. For unconditional image generation, inverse noise correction improves FID of generated images at lower FLOPs/image.

Real-world image super-resolution (Real-SR) has been revolutionized by leveraging the powerful generative priors of large-scale diffusion and flow-based models. However, fine-tuning these models on limited LR-HR pairs often precipitates "prior collapse" that the model sacrifices its inherent generative richness to overfit specific training degradations. This issue is further exacerbated in one-step generation, where the absence of multi-step refinement leads to significant trajectory drift and artifact generation. In this paper, we propose Allo{SR}^2, a novel framework that rectifies one-step SR trajectories via allomorphic generative flows to maintain high-fidelity generative realism. Specifically, we utilize Signal-to-Noise Ratio (SNR) Guided Trajectory Initialization to establish a physically grounded starting state by aligning the degradation level of LR latent features with the optimal anchoring timestep of the pre-trained flow. To ensure a stable, curvature-free path for one-step inference, we propose Flow-Anchored Trajectory Consistency (FATC), which enforces velocity-level supervision across intermediate states. Furthermore, we develop Allomorphic Trajectory Matching (ATM), a self-adversarial alignment strategy that minimizes the distributional discrepancy between the SR flow and the generative flow in a unified vector field. Extensive experiments on both synthetic and real-world benchmarks demonstrate that Allo{SR}^2 achieves state-of-the-art performance in one-step Real-SR, offering a superior balance between restoration fidelity and generative realism while maintaining extreme efficiency.

We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes its target vector field in closed-form. The key ingredient behind RFM is the construction of a relatively simple premetric for defining target vector fields, which encompasses the existing Euclidean case. To extend to general geometries, we rely on the use of spectral decompositions to efficiently compute premetrics on the fly. Our method achieves state-of-the-art performance on many real-world non-Euclidean datasets, and we demonstrate tractable training on general geometries, including triangular meshes with highly non-trivial curvature and boundaries.

We present Flowception, a novel non-autoregressive and variable-length video generation framework. Flowception learns a probability path that interleaves discrete frame insertions with continuous frame denoising. Compared to autoregressive methods, Flowception alleviates error accumulation/drift as the frame insertion mechanism during sampling serves as an efficient compression mechanism to handle long-term context. Compared to full-sequence flows, our method reduces FLOPs for training three-fold, while also being more amenable to local attention variants, and allowing to learn the length of videos jointly with their content. Quantitative experimental results show improved FVD and VBench metrics over autoregressive and full-sequence baselines, which is further validated with qualitative results. Finally, by learning to insert and denoise frames in a sequence, Flowception seamlessly integrates different tasks such as image-to-video generation and video interpolation.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled via the tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improves on the accuracy -- especially on the tails of the distribution -- and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

Continuous image editing aims to provide slider-style control of edit strength while preserving source-image fidelity and maintaining a consistent edit direction. Existing learning-based slider methods typically rely on auxiliary modules trained with synthetic or proxy supervision. This introduces additional training overhead and couples slider behavior to the training distribution, which can reduce reliability under distribution shifts in edits or domains. We propose FlowSlider, a training-free method for continuous editing in Rectified Flow that requires no post-training. FlowSlider decomposes FlowEdit's update into (i) a fidelity term, which acts as a source-conditioned stabilizer that preserves identity and structure, and (ii) a steering term that drives semantic transition toward the target edit. Geometric analysis and empirical measurements show that these terms are approximately orthogonal, enabling stable strength control by scaling only the steering term while keeping the fidelity term unchanged. As a result, FlowSlider provides smooth and reliable control without post-training, improving continuous editing quality across diverse tasks.