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arXiv Machine Learning

When Can Conditional Flow Matching Replace Pointwise Negative Log-Likelihood?

The paper investigates when conditional flow matching (CFM) can replace pointwise negative log-likelihood (NLL) calculations. It shows that for linear Gaussian paths, the endpoint NLL can be exactly decomposed into entropy, a weighted CFM objective, and residual terms, meaning CFM-only estimates are exact only when these residuals cancel. The study finds that ordinary CFM is generally not a pointwise NLL estimator, and even weighted variants may not fully eliminate bias, especially in training or on‑policy settings, with experiments confirming these theoretical insights.

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arXiv Machine Learning
5d ago

Cumulative Marginal Matching for One-Step Diffusion

The paper introduces Cumulative Marginal Matching (CMM), a new objective for training few‑step diffusion and flow‑matching models. CMM treats flow‑matching as a sequence of intermediate marginal distributions and directly optimizes the cumulative Wasserstein‑2 discrepancy between the base and few‑step models across the entire trajectory. It derives a tractable surrogate for this objective, shows that Shortcut‑CSL is a first‑order approximation of CMM, and reports improved generation quality on standard benchmarks under the same training budget.

By Paribesh Regmi, Rui Li
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arXiv AI
5d ago

Preconditioned Flow Matching

Preconditioned Flow Matching introduces a precondition-then-match framework that transforms target distributions into more isotropic representations before training flow matching models. By reshaping intermediate distributions, the method improves conditioning, leading to better low-eigenvalue recovery and enhanced performance metrics such as FID, MMD, precision, and recall across Gaussian, Gaussian-mixture, and high-resolution image datasets. The approach is theoretically justified and empirically validated, with ablations showing gains stem from improved geometry rather than extra parameters.

By Shadab Ahamed, Eshed Gal, Md Shahriar Rahim Siddiqui, Simon Ghyselincks, Moshe Eliasof, Eldad Haber
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arXiv Statistics ML
Oct 26

Compatible Likelihoods for Flow Matching on Manifolds

The paper investigates flow matching on manifolds, focusing on the 1D flat torus. It identifies a failure mode caused by a property called compatibility, where a likelihood-based flow matching objective can be globally optimized by a velocity field that actually pushes samples away from the data distribution. The authors propose a new compatible objective built from an exponential family over endpoints, which restricts the velocity field to feasible values on compact manifolds and improves performance on high-dimensional product tori, geospatial benchmarks on the sphere, and a large human pose dataset.

By Lucas Ng, Georgios Batzolis, Mark Girolami
diffusionbenchmarks
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arXiv Machine Learning
Oct 22

Minimax-Optimal Predictive Flow Matching under Distribution Drift

The paper introduces DyProd-FM, a method for predictive flow matching that refits flow matching models on dyadic historical prefixes and selects among them using a sleeping Prod master. It achieves dynamic regret bounds of “~O(min{N_ω+1,1+√{TΩ}}) and ~O(min{N_μ+1,1+T^{1/3}V_μ^{2/3}}) in relative velocity risk variation Ω and target‑law variation V_μ, respectively, without requiring a drift budget. These bounds are shown to be optimal up to logarithmic factors for fixed, possibly nonconvex, neural classes.

By Aadithya Srikanth, Vaneet Aggarwal
diffusion
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