arXiv Machine Learning
Correcting CondOT: Exact Finite-Step Sampling in Gaussian Flow Matching
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arXiv Machine Learning
Sep 23
Gaussian Flow-Matching Schedules: Implications for Sampling and Training
The paper studies how flow‑matching schedules influence sampling dynamics and regression variance. For centered commuting Gaussians, it shows that a direction‑dependent schedule splits into a variance path that determines intermediate laws and a factorization that keeps the flow unchanged while controlling irreducible regression variance. The authors analyze finite‑step Euler accuracy, derive a drift bound for exact N‑step sampling, and provide closed‑form factorizations that either minimize time‑averaged regression variance or keep it constant along a fixed path.
arXiv Machine Learning
Jul 16
Convergence Rates for Distribution Matching with Sliced Optimal Transport
arXiv:2602. 10691v2 Announce Type: replace-cross Abstract: We study the slice-matching scheme, an efficient iterative method for distribution matching based on sliced optimal transport.
arXiv Statistics ML
2d ago
Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Support
arXiv:2609.38918v1 Announce Type: cross Abstract: Flow Matching (FM) learns a velocity field whose ODE transports a simple source distribution to a target law. Existing finite-sample theory largely t...
arXiv Machine Learning
Jul 16
Heavy-Tailed Flow Matching via Random Clocks
arXiv:2607. 13841v1 Announce Type: new Abstract: Heavy-tailed data arise in many domains where rare events carry disproportionate importance, such as imbalanced image datasets, financial returns, and weather extremes.
arXiv Machine Learning
Sep 11
Prediction--Loss Alignment for Sampler--Robust Flow Matching Training
The paper examines the common practice in diffusion and flow matching of predicting the clean signal, converting it to a velocity, and training with a velocity-space loss. It shows that this conversion can cause unstable optimization due to singular endpoint amplification, but that prediction–loss alignment removes this source of non‑integrability and ensures a finite second moment for all timesteps, even with uniform sampling. Experiments confirm that aligned objectives remain trainable across different samplers, reconciling theoretical concerns with empirical success.
Hugging Face Trending Papers
Jun 23
A Time-Reparameterized Cumulative Intensity Extrapolation Sampler for Discrete Flow Matching
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.