Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
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Building Normalizing Flows with Stochastic Interpolants
36 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that interpolates between the base and the target in finite time. Unlike conventional normalizing flow inference methods based the maximum likelihood principle, which require costly backpropagation through ODE solvers, our interpolant approach leads to a simple quadratic loss for the velocity itself which is expressed in terms of expectations that are readily amenable to empirical estimation. The flow can be used to generate samples from either the base or target, and to estimate the likelihood at any time along the interpolant. In addition, the flow can be optimized to minimize the path length of the interpolant density, thereby paving the way for building optimal transport maps. In situations where the base is a Gaussian density, we also show that the velocity of our normalizing flow can also be used to construct a diffusion model to sample the target as well as estimate its score. However, our approach shows that we can bypass this diffusion completely and work at the level of the probability flow with greater simplicity, opening an avenue for methods based solely on ordinary differential equations as an alternative to those based on stochastic differential equations. Benchmarking on density estimation tasks illustrates that the learned flow can match and surpass conventional continuous flows at a fraction of the cost, and compares well with diffusions on image generation on CIFAR-10 and ImageNet $32\times32$. The method scales ab-initio ODE flows to previously unreachable image resolutions, demonstrated up to $128\times128$.
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- abstract A generative model based on a continuous-time normalizing flow between any pair of base and target probability densities is proposed. The velocity field of this flow is inferred from the probability current of a time-dependent density that interpolates between the base and the target in finite time. Unlike conventional normalizing flow inference methods based the maximum likelihood principle, which require costly backpropagation through ODE solvers, our interpolant approach leads to a simple quadratic loss for the velocity itself which is expressed in terms of expectations that are readily ame
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Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
ReConText3D is the first replay-memory framework for continual text-to-3D generation that prevents catastrophic forgetting on new textual categories while preserving quality on previously seen classes.
Marginal-conditioned bridges enable training-free sampling from Flow Language Models by drawing clean one-hot endpoints from factorized posteriors and using Ornstein-Uhlenbeck bridges, preserving token marginals and reducing denoising error versus conditional-mean bridges.
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
HorizonDrive enables stable long-horizon autoregressive driving simulation via anti-drifting teacher training with scheduled rollout recovery and teacher rollout distillation.
Existence and uniqueness of cyclically monotone zero-couplings are established for arbitrary pairs of infinite measures in M_0(R^d) under a Hausdorff-dimension condition, with the tail limit of such couplings for regularly varying distributions coinciding with the unique proper zero-coupling of the
A general framework reduces flow matching on symmetric spaces to flow matching on a Lie algebra subspace, linearizing geodesics.
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
FAN achieves state-of-the-art offline RL performance on robotic tasks by anchoring flow policies and using single-sample noise-conditioned Q-learning, with proven convergence and reduced runtimes.
TabGRAA enables self-improving tabular language models through iterative group-relative advantage alignment using modular automated quality signals like distinguishability classifiers.
UniGeo unifies geometric guidance across three levels in video models to reduce geometric drift and improve consistency in camera-controllable image editing.
A conditional diffusion model using proprioception and multi-contact touch produces metric-scale, physically consistent 3D object reconstructions under hand occlusion.
GVCC achieves the lowest LPIPS on UVG at bitrates down to 0.003 bpp by encoding stochastic innovations in a marginal-preserving stochastic process derived from a pretrained rectified-flow video model, with 65% LPIPS reduction over DCVC-RT.
SVAR-FM uses simulator clamping to produce interventional distributions and flow matching to identify time series causal structures, with an error bound that predicts sign reversal of causal effects below a simulator accuracy threshold.
Discrete flow matching on Z_m^d achieves non-asymptotic KL bounds for early-stopped targets and explicit TV convergence to the true target under an approximation error assumption, with improved scaling in dimension d and vocabulary size m.
Conservative flows generate by running probability-preserving stochastic dynamics initialized at data points rather than noise, using corrected Langevin or predictor-corrector mechanisms on top of any pretrained flow model and showing gains on Swiss-roll, ImageNet-256 and Oxford Flowers-102.
SDFlow learns a global transport map via similarity-driven flow matching in VQ latent space, using low-rank manifold decomposition and a categorical posterior to handle discreteness, yielding SOTA long-horizon performance and inference speedups.
FES-FM applies reduced flow matching with a Hessian-derived prior to directly sample free energy surfaces in collective variable space, claiming lower computational cost and higher accuracy per unit time than standard methods.
Neural networks learn the score of the probability density on Bohmian trajectories to recover exact Schrödinger dynamics via self-consistent minimization for nodeless wave functions, demonstrated on double-well splitting and Morse chain vibrations.
Allo{SR}^2 rectifies one-step super-resolution trajectories with allomorphic generative flows via SNR initialization, velocity supervision, and self-adversarial matching to deliver state-of-the-art fidelity and realism.
Fisher Decorator refines flow policies in offline RL via a local transport map and Fisher-matrix quadratic approximation of the KL constraint, yielding controllable error near the optimum and SOTA benchmark results.
FreqFlow introduces frequency-aware conditioning and a two-branch architecture to flow matching, reaching FID 1.38 on ImageNet-256 and outperforming DiT and SiT.
LiveMoments restores reselected key photos in Live Photos via reference-guided diffusion and motion alignment, yielding higher perceptual quality and fidelity than prior methods especially under fast motion.
citing papers explorer
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What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matching
Data geometry makes time identifiable from noisy interpolants at rate O(1/sqrt(d-k)), rendering the time-blindness gap asymptotically negligible relative to coupling variance.
-
Generative Modeling with Flux Matching
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
-
ReConText3D: Replay-based Continual Text-to-3D Generation
ReConText3D is the first replay-memory framework for continual text-to-3D generation that prevents catastrophic forgetting on new textual categories while preserving quality on previously seen classes.
-
Sampling from Flow Language Models via Marginal-Conditioned Bridges
Marginal-conditioned bridges enable training-free sampling from Flow Language Models by drawing clean one-hot endpoints from factorized posteriors and using Ornstein-Uhlenbeck bridges, preserving token marginals and reducing denoising error versus conditional-mean bridges.
-
One-Step Generative Modeling via Wasserstein Gradient Flows
W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.
-
HorizonDrive: Self-Corrective Autoregressive World Model for Long-horizon Driving Simulation
HorizonDrive enables stable long-horizon autoregressive driving simulation via anti-drifting teacher training with scheduled rollout recovery and teacher rollout distillation.
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Zero-couplings of infinite measures with cyclically monotone support and multivariate regular variation
Existence and uniqueness of cyclically monotone zero-couplings are established for arbitrary pairs of infinite measures in M_0(R^d) under a Hausdorff-dimension condition, with the tail limit of such couplings for regularly varying distributions coinciding with the unique proper zero-coupling of the
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Flow Matching on Symmetric Spaces
A general framework reduces flow matching on symmetric spaces to flow matching on a Lie algebra subspace, linearizing geodesics.
-
Generative Modeling with Orbit-Space Particle Flow Matching
OGPP is a particle flow-matching method using orbit-space canonicalization and geometric paths that achieves lower error and fewer steps than prior approaches on 3D benchmarks.
-
Towards Efficient and Expressive Offline RL via Flow-Anchored Noise-conditioned Q-Learning
FAN achieves state-of-the-art offline RL performance on robotic tasks by anchoring flow policies and using single-sample noise-conditioned Q-learning, with proven convergence and reduced runtimes.
-
Self-Improving Tabular Language Models via Iterative Group Alignment
TabGRAA enables self-improving tabular language models through iterative group-relative advantage alignment using modular automated quality signals like distinguishability classifiers.
-
UniGeo: Unifying Geometric Guidance for Camera-Controllable Image Editing via Video Models
UniGeo unifies geometric guidance across three levels in video models to reduce geometric drift and improve consistency in camera-controllable image editing.
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Physically Grounded 3D Generative Reconstruction under Hand Occlusion using Proprioception and Multi-Contact Touch
A conditional diffusion model using proprioception and multi-contact touch produces metric-scale, physically consistent 3D object reconstructions under hand occlusion.
-
GVCC: Zero-Shot Video Compression via Codebook-Driven Stochastic Rectified Flow
GVCC achieves the lowest LPIPS on UVG at bitrates down to 0.003 bpp by encoding stochastic innovations in a marginal-preserving stochastic process derived from a pretrained rectified-flow video model, with 65% LPIPS reduction over DCVC-RT.
-
Intervention-Based Time Series Causal Discovery via Simulator-Generated Interventional Distributions
SVAR-FM uses simulator clamping to produce interventional distributions and flow matching to identify time series causal structures, with an error bound that predicts sign reversal of causal effects below a simulator accuracy threshold.
-
Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions
Discrete flow matching on Z_m^d achieves non-asymptotic KL bounds for early-stopped targets and explicit TV convergence to the true target under an approximation error assumption, with improved scaling in dimension d and vocabulary size m.
-
Conservative Flows: A New Paradigm of Generative Models
Conservative flows generate by running probability-preserving stochastic dynamics initialized at data points rather than noise, using corrected Langevin or predictor-corrector mechanisms on top of any pretrained flow model and showing gains on Swiss-roll, ImageNet-256 and Oxford Flowers-102.
-
SDFlow: Similarity-Driven Flow Matching for Time Series Generation
SDFlow learns a global transport map via similarity-driven flow matching in VQ latent space, using low-rank manifold decomposition and a categorical posterior to handle discreteness, yielding SOTA long-horizon performance and inference speedups.
-
Free Energy Surface Sampling via Reduced Flow Matching
FES-FM applies reduced flow matching with a Hessian-derived prior to directly sample free energy surfaces in collective variable space, claiming lower computational cost and higher accuracy per unit time than standard methods.
-
Quantum Dynamics via Score Matching on Bohmian Trajectories
Neural networks learn the score of the probability density on Bohmian trajectories to recover exact Schrödinger dynamics via self-consistent minimization for nodeless wave functions, demonstrated on double-well splitting and Morse chain vibrations.
-
Allo{SR}$^2$: Rectifying One-Step Super-Resolution to Stay Real via Allomorphic Generative Flows
Allo{SR}^2 rectifies one-step super-resolution trajectories with allomorphic generative flows via SNR initialization, velocity supervision, and self-adversarial matching to deliver state-of-the-art fidelity and realism.
-
Fisher Decorator: Refining Flow Policy via a Local Transport Map
Fisher Decorator refines flow policies in offline RL via a local transport map and Fisher-matrix quadratic approximation of the KL constraint, yielding controllable error near the optimum and SOTA benchmark results.
-
Frequency-Aware Flow Matching for High-Quality Image Generation
FreqFlow introduces frequency-aware conditioning and a two-branch architecture to flow matching, reaching FID 1.38 on ImageNet-256 and outperforming DiT and SiT.
-
LiveMoments: Reselected Key Photo Restoration in Live Photos via Reference-guided Diffusion
LiveMoments restores reselected key photos in Live Photos via reference-guided diffusion and motion alignment, yielding higher perceptual quality and fidelity than prior methods especially under fast motion.
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Region-Constrained Group Relative Policy Optimization for Flow-Based Image Editing
RC-GRPO-Editing constrains GRPO exploration to editing regions via localized noise and attention rewards, improving instruction adherence and non-target preservation in flow-based image editing.
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Monte Carlo Event Generation with Continuous Normalizing Flows
Continuous normalizing flows improve unweighting efficiency in Monte Carlo event generation for high-jet-multiplicity collider processes by factors up to 184, with wall-time gains of about ten when combined with coupling-layer flows.
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Mean Flows for One-step Generative Modeling
MeanFlow uses a derived identity between average and instantaneous velocities to train one-step flow models, achieving FID 3.43 on ImageNet 256x256 with 1-NFE from scratch.
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MAGI-1: Autoregressive Video Generation at Scale
MAGI-1 is a 24B-parameter autoregressive video world model that predicts denoised frame chunks sequentially with increasing noise to enable causal, scalable, streaming generation up to 4M token contexts.
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DanceGRPO: Unleashing GRPO on Visual Generation
DanceGRPO applies GRPO to visual generation tasks to achieve stable policy optimization across diffusion models, rectified flows, multiple tasks, and diverse reward models, outperforming prior RL methods.
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CaloArt: Large-Patch x-Prediction Diffusion Transformers for High-Granularity Calorimeter Shower Generation
CaloArt achieves top FPD, high-level, and classifier metrics on CaloChallenge datasets 2 and 3 while keeping single-GPU generation at 9-11 ms per shower by combining large-patch tokenization, x-prediction, and conditional flow matching.
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Neural Posterior Estimation of Terrain Parameters from Radar Sounder Data
Neural posterior estimation trained on simulated radar data enables probabilistic inference of terrain parameters from real Mars radar sounder profiles while conditioning on reference surface assumptions.
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SubFlow: Sub-mode Conditioned Flow Matching for Diverse One-Step Generation
SubFlow restores full mode coverage in one-step flow matching by conditioning on sub-modes from semantic clustering, yielding higher diversity on ImageNet-256 while preserving FID.
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Efficient Hierarchical Implicit Flow Q-learning for Offline Goal-conditioned Reinforcement Learning
Proposes mean flow policies and LeJEPA loss to overcome Gaussian policy limits and weak subgoal generation in hierarchical offline GCRL, reporting strong results on OGBench state and pixel tasks.
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Exploring Motion-Language Alignment for Text-driven Motion Generation
MLA-Gen advances text-driven motion synthesis by aligning global motion patterns with fine-grained text semantics and mitigating attention sink effects via new masking techniques.
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An AI-based Detector Simulation and Reconstruction Model for the ALEPH Experiment at LEP
Parnassus faithfully reproduces the ALEPH detector response at event, jet, and particle levels for clean e+e- to Z to qqbar events.
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Flow Matching Guide and Code
Flow Matching is a generative modeling framework with mathematical foundations, design choices, extensions, and open-source PyTorch code for applications like image and text generation.