Flow-Based Generative Modeling

Diffusion and continuous-flow generative models achieve high-quality generation, and their deterministic sampling can be formulated as solving learned ODE dynamics. However, accurate ODE discretization often requires many steps, making efficient few-step generation a key challenge. Among acceleration strategies, reflow-based distillation simplifies teacher ODE trajectories so that a student model can approximate the teacher transport with fewer steps. We identify a theoretical limitation of this paradigm, namely that trajectory matching can under-determine the distribution induced by the student model. In particular, two student models can attain the same trajectory-matching loss while inducing different endpoint marginal distributions, which may lead to different generation quality. To address this limitation, we introduce a marginal-alignment regularizer that penalizes the discrepancy between the student-induced marginal and the corresponding teacher marginal at the endpoint of each distillation interval. The regularizer is computed by tracking log-density changes along the ODE induced by the student model and evaluating scores from the frozen teacher model, without requiring auxiliary trainable networks or adversarial optimization. The resulting framework applies uniformly to the reflow family, including vanilla reflow and piecewise reflow. We further prove a telescoping total-variation bound showing that local marginal alignment controls the final-time discrepancy between the student-induced and teacher-induced distributions. Experiments on benchmark backbones demonstrate the effectiveness of the proposed method for few-step generation.

Structured reasoning requires making and revising interdependent decisions to reach a globally consistent solution. Existing architectures struggle with this: autoregressive models commit sequentially and cannot revise earlier decisions, while masked diffusion models often require careful decoding schemes to coordinate interdependent predictions. We introduce Flow Reasoning Models (FRMs), a novel framework for structured reasoning that adapts continuous flows over discrete structured outputs with a simple recurrent refinement mechanism. By self-conditioning a flow model on its own past outputs, we turn one-shot denoising into iterative solution refinement. This lets FRMs make and revise decisions in parallel, efficiently coordinating interdependent choices across solutions. Yet conventional self-conditioning becomes unreliable at greater recurrent depth due to exposure bias between one-step training predictions and recursively generated inference states. We address this mismatch with Fixed-Point Forcing (FPF), which trains FRMs on states produced by their own inference dynamics while preserving the standard flow-matching objective. FRMs achieve solve rates of $99.5\%$, $100.0\%$, and $99.9\%$ on Sudoku-Extreme, Zebra, and Maze-Unique, respectively. On Sudoku-Extreme, FRMs achieve higher peak accuracy than the evaluated masked-diffusion and specialized reasoning baselines while remaining highly compute-efficient, matching the next-best method's $98.7\%$ peak solve rate with $44\times$ fewer inference FLOPs.

Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the model likelihood. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson's trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While F2D2 uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to 10x inference speedup over the fastest baseline.

World modeling requires forecasting uncertain futures while preserving information useful for downstream perception. Existing visual world models often struggle to satisfy both goals: VAE-based stochastic models operate in low-dimensional reconstruction latents, which can limit perception performance, while deterministic predictors using strong pretrained features collapse multimodal futures into a single blurry mean. In this work, we propose FlowWM, a stochastic world model that performs flow matching directly within pretrained feature space (e.g., DINOv3). This is challenging because pretrained features are substantially high-dimensional, making standard diffusion recipes suboptimal. To address this, we investigate the design choices needed for feature-space flow matching and introduce a differentiable one-step projection mechanism that enables efficient training with temporal consistency and task-driven objectives. We evaluate FlowWM on two benchmarks: a synthetic benchmark for systematic evaluation of accuracy and diversity, and a real-world benchmark FuturePerception. FlowWM improves perception performance, mode coverage, and horizon robustness, validating our proposed design for stochastic world modeling in high-dimensional feature spaces.

Masked Diffusion Models (MDMs) promise fast, parallel language generation, but their reverse transition factorises across token positions -- an approximation that breaks down in the few-step sampling regime where parallel generation ought to provide the greatest efficiency gains. Flow Language Models (FLMs) sidestep this limitation by learning a continuous flow that transports noise toward clean sequences represented in Euclidean space, inducing a flow map that can be distilled for single-step generation. However, this makes complex tasks requiring multi-step reasoning problematic for FLMs, as FLMs are forced to decode every token during generation. To address this, we introduce Masked Language Flow Models (MLFMs), which incorporate masking into FLMs using a continuous stochastic interpolant to bridge partially masked and clean sequences. This design enables conditional generation via continuous flows and allows pretrained MDMs to be converted into MLFMs through a simple, lightweight adaptation. Leveraging this flexibility, we propose a novel sampler that alternates continuous denoising with the discrete unmasking of confident tokens to better support multi-step reasoning. We evaluate our approach on GSM8K and MT-Bench and find, for the first time, that flow-based language models can be scaled to solve downstream reasoning and instruction-following tasks.

Autoregressive Transformers dominate high-quality mesh generation by producing artist-worthy topologies, yet their inherent sequential decoding induces substantial computational overhead, falling orders of magnitude slower than parallel generative models. On the other hand, while continuous diffusion and flow-matching methods support efficient parallel synthesis across a variety of domains, they cannot be directly applied to meshes: mesh connectivity is inherently discrete and incompatible with standard continuous noise injection and denoising operations. To resolve this fundamental incompatibility, we introduce a compact topology embedder that projects discrete mesh vertex positions and normals into continuous per-vertex embeddings, where the original discrete adjacency information can be faithfully recovered via spacetime distance thresholding. After pretraining and freezing this embedder, any raw mesh can be fully converted into a continuous per-vertex state space unifying position, normal, and implicit topological attributes. Built upon this novel continuous mesh representation, we present PolyFlow, a Transformer-based flow-matching framework that achieves fully parallel vertex state denoising conditioned on extracted point-cloud features. During inference, our model completes generation rapidly via an ODE solver, and supports explicit, precise control over output mesh resolution by directly specifying the target vertex count. Extensive evaluations on the Toys4K benchmark demonstrate that PolyFlow surpasses state-of-the-art autoregressive baselines in both Chamfer Distance and Hausdorff Distance.

Modern image generation demands a single model that unifies diverse capabilities, including text-to-image (T2I), local editing, and global editing. However, these capabilities are rarely naturally aligned and often conflict. For instance, editing tends to degrade T2I performance, while global and local editing interfere with each other. Consequently, effectively composing these capabilities has become a central challenge for image generation model training. To tackle this, we introduce DanceOPD, an on-policy generative field distillation framework for flow-matching models that routes each sample to one capability field, queries one low-noise student-induced state, and trains with a simple velocity MSE objective. With each capability source defined as a velocity field over the shared flow state space, the student learns from fields queried on its own rollout states to compose expert capabilities. This formulation also absorbs operator-defined fields such as classifier-free guidance. Comprehensive experiments on T2I, editing, realism-field absorption, and CFG absorption show that our approach improves multi-capability composition, strengthening target capabilities while preserving anchor generation quality. We believe this work establishes a practical route for generative field distillation in flow-matching models.

State-of-the-art flow models generate stunning images from text or image prompts. However, they suffer from diversity collapse when generating multiple samples under the same conditioning. Existing methods address this issue via either latent guidance, which has limited effectiveness, or sample selection, which relies on external reward models that incur significant inference-time overhead. In this work, we introduce an efficient, training-free self-guidance mechanism to mitigate diversity collapse without requiring additional reward models. Specifically, we disperse the internal features of the flow model during batch generation with feature self-guidance. Further, to keep the features close to the manifold, we introduce a manifold regularization step that projects these dispersed features back onto the data manifold, ensuring diverse generation without sacrificing alignment with the input conditions. Our method integrates seamlessly as a plug-and-play module into pretrained flow models, adding only a marginal inference cost. Experiments demonstrate significant improvements in diversity while preserving fidelity across several conditional flow models, including multi-step and few-step text-to-image, depth-to-image, and reference image generation.

Normalizing Flows (NFs) are powerful generative models capable of exact density estimation and sampling. However, their strict invertibility often forces the model to exhaust its capacity on low-level pixel details, hindering the capture of high-level semantic structures. While Masked Image Modeling (MIM) has excelled in representation learning, its integration into generative pipelines has remained largely modular and disjointed. In this paper, we propose MIMFlow, a unified end-to-end framework that jointly optimizes latent semantics, pixel reconstruction, and generative flow. By employing a VAE encoder to infer semantic latent from masked images, MIMFlow achieves a principled decoupling of the generative task: the Normalizing Flow focuses on modeling a simplified, low-frequency semantic manifold, while a specialized decoder handles high-frequency synthesis. This design effectively resolves the inherent capacity bottleneck of NFs, allowing the model to prioritize global structural coherence over redundant noise. Empirical results on ImageNet 256$\times$256 show that MIMFlow-L reaches 71.3% linear probing accuracy and an FID of 2.50. Despite using only 128 tokens (50% fewer than standard models), it yields a 32.8% performance gain over similar-scale NF baselines. Our code is available at https://github.com/MCG-NJU/MIMFlow.

Non-autoregressive generation offers a powerful paradigm for iterative refinement, allowing models to recursively critique, erase and regenerate arbitrary subsets of tokens. However, existing non-autoregressive models fail to realize this potential. Masked Diffusion Models (MDMs) suffer from factorization error, causing sample quality to collapse when generating multiple tokens simultaneously. Flow Map Language Models (FMLMs) circumvent this bottleneck via joint sequence transport for excellent few-step generation, but sacrifice the inference-time flexibility of MDMs. We introduce FMLM+, a framework that bridges this gap by equipping FMLM with masking-style noise schedules. While generating the full sequence in a single step, FMLM+ simultaneously scores the global consistency of each token a posteriori. We leverage this to introduce Posterior Refinement, a novel inference-time refinement strategy that enables the model to adaptively self-correct its outputs, matching the performance of discrete baselines with 32x fewer NFEs. Across diverse benchmarks, we demonstrate that FMLM+ with Posterior Refinement improves the speed--quality tradeoff over both MDM and FMLM families, providing a scalable foundation for high-fidelity language modeling.

Generative models, particularly diffusion and score-based approaches, have recently achieved strong performance in speech enhancement, but their iterative sampling process limits real-time deployment. Flow Matching offers an efficient alternative by transporting noisy speech toward clean speech through an ordinary differential equation with few function evaluations. In this work, we propose a skip-free encoder-decoder backbone for flow-matching speech enhancement, guided by Latent Representation Alignment (LRA). Instead of relying on U-Net skip connections, which may transfer noise-correlated low-level features to the decoder, the proposed model aligns its bottleneck and decoder representations with clean latent features extracted from a frozen Descript Audio Codec encoder-decoder without quantization. This codec-aligned supervision promotes compact clean-speech representations while preserving efficient few-step inference. Experiments on WSJ0-CHiME3 and VoiceBank-DEMAND show improved PESQ and perceptual quality, especially on VoiceBank-DEMAND, using only five function evaluations.

Data preparation pipelines improve data quality in machine learning by transforming raw tables into learning-ready data through sequential cleaning and feature transformation operators. However, automatically constructing such pipelines is computationally difficult because operator sequences are combinatorial and end-to-end evaluation is expensive. Existing state-of-the-art (SOTA) Multi-DQN methods still face three key limitations: decoupled value estimators weaken long-horizon credit assignment, dataset context is only weakly injected into the policy, and exploration is inefficient in a sparse search space with many invalid states. To address these issues, we propose FlowPipe, a unified framework that formulates pipeline synthesis as conditional probabilistic flow generation over a directed acyclic graph. FlowPipe uses Conditional Generative Flow Networks (C-GFlowNets) with a Trajectory Balance objective to connect terminal validation rewards with early pipeline decisions. It further introduces Deep Semantic Modulation through Feature-wise Linear Modulation (FiLM), allowing LLM-derived logical priors to condition the policy's internal activations according to dataset semantics. In addition, FlowPipe incorporates failure awareness into the flow objective to avoid invalid states and concentrate search on high-potential regions. Experiments on two benchmark suites with 74 real-world datasets show that FlowPipe outperforms SOTA baselines, improving accuracy by 11.96% on average and achieving 12.5x faster training convergence. Source code is available at https://github.com/KunyuNi/FlowPipe.

A growing family of training-free solvers -- FlowDPS, FLOWER, PnP-Flow and their diffusion ancestors (DPS, DAPS) -- repurpose a pretrained flow-matching prior to solve imaging inverse problems by adding a measurement-guidance term to the deterministic probability-flow ODE. Despite strong empirical results, what these per-step corrections actually approximate -- and how far the resulting samples are from the true posterior $p(x\mid y)$ -- has not been characterized. We give a posterior-transport account of flow-based inverse problem solving. Our starting point is a simple but consequential fact: for a \emph{deterministic} flow prior, Bayesian conditioning is realized entirely by a \emph{reweighting of the source distribution}, not by a drift correction; pushing the reweighted source through the \emph{unmodified} velocity field yields exact posterior samples. From this we show that trajectory-guidance solvers can be read as the minimum-kinetic-energy \emph{correction} field needed to morph the unconditional source into the posterior, and that FlowDPS / FLOWER / PnP-Flow correspond to distinct zeroth-order / Gaussian / proximal approximations of this single object; we bound the resulting posterior bias in Wasserstein distance. A controlled $2$D study with a closed-form posterior confirms the theory decisively: source reweighting matches the true posterior to the Monte-Carlo floor on every metric, whereas trajectory guidance incurs $200$--$800\times$ larger error and collapses posterior modes, \emph{regardless of guidance strength}. Guided by the analysis we propose a cheap, principled velocity-correction solver that is competitive across two in-domain priors (AFHQ, CelebA) and two out-of-distribution settings while, unlike point-estimate source-space optimizers, producing diverse posterior samples with uncertainty that correlates with reconstruction error.

Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as $τ$-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied. To address this gap, we propose the Time-Reparameterized Cumulative Intensity Extrapolation (TR-CIE) sampler, which aims to improve sampling quality when function evaluations are restricted. TR-CIE consists of two components. First, a schedule-based time reparameterization rescales the time grid according to the noise schedule. Under standard factorized DFM rate parameterizations, this transformation of variables absorbs the schedule-dependent growth term and mitigates stiffness near the terminal sampling stage. Second, we introduce a cumulative-intensity extrapolation updating rule. By reusing cached model outputs from the previous step as a history term, this improves the approximation of stepwise cumulative intensities on the resulting non-uniform time grid. We provide a theoretical analysis that bounds the local approximation error of cumulative intensities and establishes convergence results. The resulting sampler requires one NFE per step and introduces no additional model evaluations compared to the standard $τ$-leaping sampler. Extensive experiments on synthetic tasks, text generation, and text-to-image benchmarks demonstrate that our method improves sampling quality under limited NFE.

Meshes are among the most common 3D scene representations, but directly generating meshes is challenging because the representation contains important symmetries, including permutation invariance of faces and vertices. MeshFlow learns to generate triangle meshes directly as triangle soups, avoiding the need to serialize meshes into long autoregressive sequences. We adopt equivariant optimal-transport flow matching models that respect the key symmetries of triangle soups: arbitrary permutations of faces and permutations of the vertices within each face. Toward this goal, we propose a simple yet effective modification to the Diffusion Transformer architecture, resulting in a scalable network capable of modeling a velocity field while maintaining the desired equivariance. We further introduce an optimal-transport-based training objective that improves convergence by eliminating supervision signals that violate these symmetries. MeshFlow achieves mesh quality comparable to state-of-the-art autoregressive mesh generators while providing about an 18$\times$ speedup during inference. Project page is at https://qiisun.github.io/MeshFlow/.

Cross-embodiment data have become central to training robotic foundation models. To leverage such heterogeneous data, we focus on flow-based object manipulation, where robot flows (robot velocity fields) serve as embodiment-agnostic motion representations. Previous studies do not formulate robot flows as dense velocity fields, but as displacements of sparse keypoints, even though dense velocity fields better match the continuous-time nature of motions. To address this, we propose Flow as Flow, a framework that models robot flows as probability flows based on a flow matching formulation. By naturally modeling such velocity fields within this formulation, our method achieves efficient and high-quality robot flow generation. Across standard benchmarks, our method outperforms representative baseline methods on standard metrics, while achieving approximately 24$\times$ faster generation than standard flow matching. Furthermore, through real-world experiments evaluating 9 methods with 260 trials per method across 13 manipulation tasks, we show that our method achieves a higher average success rate than the baseline methods.

Unifying speech, sound, and music generation in one model is hindered by tradeoffs between fidelity, end-to-end training, in-context conditioning, and variable-length synthesis that no current paradigm fully resolves. To address this challenge, we present AudioCALM, a universal audio generation framework that extends autoregressive (AR) next-token prediction from discrete tokens to continuous audio latents: a thin flow-matching head replaces the softmax to predict rectified-flow velocities at each position, and a block-causal AR-Flow attention pattern produces arbitrary-length output. Joint training of multiple audio generation tasks faces an asymmetric text--audio mismatch: speech transcripts align to specific time spans and demand tight, time-aligned attention, whereas sound and music captions describe only overall semantics and rely on diffuse, holistic attention; mixing the two disproportionately degrades sound and music generation. We address this asymmetry at two levels: a data reformulation strategy that unifies all three tasks under a single description-style conditioning interface, and a novel architecture Asymmetric Mixture-of-Modality-Experts (A-MoME), which adds a dedicated residual expert for speech while sound and music share the backbone, incurring no inference overhead on non-speech inputs. Experimental results demonstrate that AudioCALM matches modality-specific state-of-the-art and outperforms prior unified baselines on speech, sound, and music generation benchmarks.

Physical simulations for intricate geometries with path-dependent constitutive models face difficulties due to the enormous computational cost they require. Recently, the emergence of generative AI models, which succeed in image and video synthesis tasks, has provided a promise to further improve simulations. Although U-Net-based denoising diffusion probabilistic models (DDPMs) have been adopted for elastic stress field generation, they typically require hundreds of sampling steps, and applications of generative models to path-dependent, e.g. plastic, stress fields remain very limited. In this work, we propose a novel flow matching (FM) model based on a transformer backbone for high-resolution path-dependent stress field generation with stochastic loading-unloading paths and geometry. The proposed model operates within the latent space of a variational autoencoder (VAE) and formulates the simulation of plastic fields as a video synthesis task, directly generating the stress fields across all time steps. Meanwhile, we design a non-Gaussian source distribution for flow matching, such that crossings among conditional transport paths are reduced during training. This enables our model to generate satisfactory samples in one step without relying on distillation. In addition, we introduce token-level loading embeddings and two auxiliary networks to further enhance the model performance in path-dependent simulation. The results demonstrate that, even with a limited training dataset, our model can accurately generate high-resolution path-dependent fields. It is much more computationally efficient than finite element analysis, providing a speedup of 6 to 7 times over FEM on CPUs and approximately two orders of magnitude speedup on consumer-grade GPUs.

We propose NullFlow, a principled framework for one-step generative image reconstruction. Our key idea is to confine the generative flow to a measurement-consistent subspace. Because the flow never leaves this subspace, NullFlow needs no separate data-fidelity corrections, unlike existing solvers. NullFlow samples in a single network evaluation by learning the flow's average velocity, avoiding the step-by-step integration of traditional flow matching methods. We prove that the average velocity of this constrained flow yields a training objective whose global minimizer is a one-step posterior sampler. We show on image inpainting that NullFlow matches state-of-the-art diffusion solvers while cutting inference from hundreds of network evaluations to one.

Diffusion and flow-based generative models produce strong images, yet their controllability remains largely endpoint-centric: users specify conditions and receive final outputs, while the intermediate generative dynamics remain hidden. Recent methods have begun to exploit generation order and process decomposition to improve sample quality, but still treat intermediate states as internal computation rather than objects for interaction. We propose Trajectory Forcing (TF), a trajectory-centric framework that makes the generation path explicit, semantic, and editable. TF organizes synthesis as a sequence of semantically structured stages, progressing from global layout to object-, part-, and detail-level representations. Each stage produces a decodable latent state that can be inspected, evaluated, and locally edited before the next stage begins. To instantiate this path, we derive coarse-to-fine teacher hierarchies by clustering pretrained visual representations such as DINOv2, and train a hierarchy-conditioned one-step flow-matching model at each level. We further introduce trajectory-aware metrics that measure structural consistency and local controllability beyond endpoint quality metrics such as FID. Experiments show that TF achieves competitive sample quality while exposing coherent intermediate states and supporting localized edits across semantic levels. By shifting the focus from final images to the generative path itself, TF opens a route toward controllable, trajectory-aware image synthesis.

Principled regression for stochastic processes is a long-standing challenge with deep connections to scientific inverse problems. We introduce Flow Annealing Posterior Sampling (FLAPS), to our knowledge the first function-space posterior sampling framework that unifies stochastic-process regression and PDE inverse problems. Built on pretrained function-space flow-matching priors, FLAPS enables likelihood-guided posterior inference from sparse and noisy observations, supports variable query discretizations, and avoids explicit prior-density evaluation. Its Langevin correction uses a low-rank covariance preconditioner to exploit dominant function-space correlations across discretizations. Across Gaussian and non-Gaussian stochastic-process regression benchmarks and diverse PDE inverse problems, FLAPS produces coherent posterior samples with well-calibrated uncertainty quantification, significantly outperforming existing functional regression baselines and achieving competitive or better noisy PDE inverse performance than diffusion-based posterior samplers while reducing test-time sampling cost.

Robots must generate trajectories that remain faithful to learned expert behavior while satisfying safety constraints and task-specific objectives specified only at inference time. We formulate constrained trajectory generation for pretrained diffusion and flow-matching policies as Bayesian posterior sampling, with the learned demonstration distribution as a prior and an inference-time, cost-derived likelihood tilting it toward feasible, optimal trajectories. To sample from this posterior without any retraining of the base policy, we leverage the Feynman--Kac corrector framework, originally formulated for diffusion models, and extend it to deterministic flow-matching policies. The result is a unified, inference-time, retraining-free sampler for diffusion and flow policies. We validate the approach on pretrained Diffusion Policy, GR00T-N1.6, and $π_{0.5}$ checkpoints across simulated and real-world manipulation tasks, including planning around non-convex obstacles introduced at inference time, and show improvements over the base $π_{0.5}$ on zero-shot tasks.

Synthetic tabular data enables microdata sharing in regulated domains, yet deploying continuous-time generative models requires balancing analytical utility, disclosure risk, and computational cost. Latent-space flow models are flexible, but theoretical equivalences across learning targets, probability paths, and sampling dynamics can translate into different behaviour under finite-step integration and explicit compute budgets. We present an empirical study of tabular latent flow models across seven datasets, evaluating velocity, score, noise, and posterior matching objectives under optimal transport (OT) and variance-preserving (VP) paths, ODE and SDE sampling, and varying integration budgets. Our contributions are threefold: (1) we show that the learning target largely determines the utility-risk operating regime, with velocity and posterior matching tending to yield higher utility, while score and noise matching tend to achieve lower disclosure risk; (2) we demonstrate that configuration and sampling choices shift performance, with midpoint often improving distributional fidelity and OT paths often tolerating earlier stopping than VP, enabling compute savings under fixed budgets or risk thresholds; and (3) we distil these findings into actionable defaults and practical configuration guidance to support pre-release model selection under disclosure risk and resource constraints. The code implementation and supplementary materials can be accessed in https://github.com/rulnasution/tabular-latent-flow/.

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/

Data editing with generative methods typically requires differentiable objectives and gradient-based search. However, these assumptions break down in flow-based settings, where edits are performed through forward and backward integration and often involve non-differentiable or black-box objectives. We introduce residual-space evolutionary optimization, a model-agnostic framework that addresses this gap by combining flow-based generative editing with evolutionary algorithms. Building on the observation that conditional flow matching (CFM) can disentangle condition-controlled factors from instance-specific residuals, our framework directly operates in residual space and separates two complementary search regimes: self-pollination performs local exploitation through feature-preserving residual refinement, and cross-pollination promotes broader exploration by recombining residuals across heterogeneous samples. As a proof of concept, we validate on MorphoMNIST, a benchmark dataset for counterfactual generation, and on crystal data, demonstrating that this exploration--exploitation decomposition provides a useful mechanism for balancing target alignment, instance preservation, and diversity, and extends beyond images to real-world scientific domains.

Most diffusion and flow-matching generators define the prior, probability path, and prediction target in the same representation space. Latent diffusion improves efficiency by moving this path into an autoencoder latent space, but the final sample is still produced by a separately trained decoder. This separation creates a mismatch: the generator is optimized for latent-space prediction, while final quality depends on how the decoder handles generated latents that may differ from clean encoder outputs. We introduce CrossFlow, a cross-space flow formulation that maps noisy latent inputs directly to pixel-space images. The key technical step is a velocity-free one-step objective: the latent trajectory defines the training path, but the supervised prediction is an image rather than a latent displacement. This lets one model act both as a one-step latent-to-pixel generator and as a decoder replacement for latent diffusion pipelines. On class-conditional ImageNet-1k at $256\times256$, CrossFlow-XL achieves 1.62 FID with one function evaluation. Ablations show that the latent encoder and pixel-space perceptual and adversarial losses are important for fidelity. These results indicate that cross-space flow objectives can combine the efficiency of latent representations with direct pixel-space supervision, without requiring a separate decoder at inference.

Recovering complete 3D representations of objects from few casual image captures remains a significant challenge. Recent 3D generative models, particularly those based on Flow-Matching (FM), can synthesize high-quality textured assets; however, they often suffer from ''synthetic bias'' where learned priors override observational evidence, alongside a lack of alignment with the observed instance. Conversely, optimization-based methods like 3D Gaussian Splatting (3DGS) provide high fidelity on visible surfaces but fail to reason about unobserved geometry. In this paper, we present FlowObject, a framework that reformulates sparse-view 3D reconstruction as a training-free, guided inverse problem. Our approach applies a dual-space guidance strategy to steer the Ordinary Differential Equation (ODE) trajectory of a flow-matching model, enabling the completion of unseen regions through learned generative priors while enforcing strict consistency with real-world observations. By integrating a 3DGS refinement stage, FlowObject further bridges the gap between ''synthetic-looking'' generative outputs and photorealistic reconstructions. Comprehensive benchmarks on synthetic and real-world datasets demonstrate that current state-of-the-art methods often struggle to achieve geometric completeness and observational consistency simultaneously, especially under severe occlusions. In contrast, our method significantly outperforms state-of-the-art generative models and optimization-based frameworks in both geometric completeness and view-dependent appearance fidelity.

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.

Conditional generative models are increasingly used as scenario generators for stochastic optimization, but standard training objectives emphasize uniform distributional fit rather than the downstream decisions induced by generated scenarios. This creates an objective mismatch: errors in statistically common regions may have little effect on decision regret, whereas errors in decision-sensitive regions can substantially change the optimal action. We propose Decision-Weighted Flow Matching (DW-FM), a regret-aligned training framework that preserves the simplicity of standard flow matching while reweighting its velocity-regression objective using decision-sensitive endpoint information. Theoretically, we connect downstream regret to pathwise velocity mismatch through a loss-induced decision discrepancy and an adjoint transport argument, yielding an ideal regret-aligned surrogate and practical endpoint-weighted objectives with regret guarantees. Empirically, we demonstrate the effectiveness of DW-FM on three CVaR-based contextual stochastic optimization benchmarks spanning synthetic portfolio, semi-real financial, and traffic-CVaR tasks, where DW-FM improves downstream regret over standard baselines.

Diffusion Flow Matching (DFM) has recently emerged as a versatile framework for generative modeling, yet its theoretical convergence properties remain only partially understood. In this work, we provide refined and novel convergence guarantees for Brownian motion based DFMs, focusing on the discretization error. Our analysis is conducted under the Kullback-Leibler (KL) divergence and the 2-Wasserstein distance. Under finite-moment conditions and a mild score integrability assumption, we derive KL convergence bounds with improved dimensional dependence compared to prior work, achieving, up to our knowledge, state-of-the-art scaling under minimal conditions. We further extend the analysis to the 2-Wasserstein distance: under an additional first-order score integrability assumption and a weak log-concavity condition, we obtain convergence guarantees with dimensional dependence consistent with the KL case.