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
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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 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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representative citing papers
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Recasts covariance shrinkage as risk minimization over stochastic interpolants between distributions, recovering known estimators via scheduling, couplings, and early stopping, and proposing a neural estimator with quadratic risk bounds.
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citing papers explorer
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Generative Modeling with Flux Matching
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Mat\'ern Noise for Triangulation-Agnostic Flow Matching on Meshes
Proposes discretized Matérn process noise for triangulation-agnostic flow matching on meshes with PoissonNet denoiser, tested on elastic states and humanoid poses for meshes exceeding one million triangles.
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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.
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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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One-Step Generative Modeling via Wasserstein Gradient Flows
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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.
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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.
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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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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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