Limit Points of Reflow with Minibatch Optimal Transport

arXiv:2608.07042 · math.PR, cs.LG, cs.NA, math.NA · Submitted 2026-08-07 · Read on arXiv

Antonin Chambolle, Johannes Hertrich

math.PR, cs.LG, cs.NA, math.NA

Submitted: 2026-08-07

Updated: 2026-08-10

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Optimal Transport — 34× in this paper · explained in 5 episodes
• Fixed Point — 23× in this paper · explained in 2 episodes
• Flow Matching — 17× in this paper · explained in 22 episodes
• Rectified Flow — 16× in this paper · explained in 3 episodes
• Monotonicity — 7× in this paper · explained in 2 episodes
• Loss Function — 6× in this paper · explained in 2 episodes
• Generative Model — 5× in this paper · explained in 2 episodes
• Generative Models — 5× in this paper · explained in 3 episodes
• Papers — 5× in this paper · explained in 3 episodes
• Distillation — 4× in this paper · explained in 2 episodes
• Generative Modeling — 4× in this paper · explained in 3 episodes
• Normalizing Flow — 3× in this paper · explained in 4 episodes
• Normalizing Flows — 3× in this paper · explained in 4 episodes
• Diffusion Model — 2× in this paper · explained in 10 episodes
• Diffusion Models — 2× in this paper · explained in 9 episodes
• Steering — 2× in this paper · explained in 2 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Knowledge Distillation — 1× in this paper · explained in 15 episodes
• Variational Bayes — 1× in this paper · explained in 2 episodes

Sources

• Expected Batch Optimal Transport Plans and Consequences for Flow Matching
• Flow Matching from Viewpoint of Proximal Operators
• Flow Matching Guide and Code
• Rectified Flow: A Marginal Preserving Approach to Optimal Transport
• Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed
• Statistical Properties of Rectified Flow
• Tessellations of Semi-Discrete Flow Matching
• On the Convergence and Straightness of Rectified Flow
• Auto-Encoding Variational Bayes
• One-Shot Generative Flows: Existence and Obstructions
• Computational and Statistical Guarantees of the c-Rectified flow

Related papers

• Sharp Deviations Bounds for Dirichlet Weighted Sums with Application to analysis of Bayesian algorithms
• Subspace Uncertainty and Sharp Sampling Thresholds on the Boolean Cube
• Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry
• Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria
• Explicit Steady-State Approximations for Parallel Server Systems with Heterogeneous Servers
• A New Bound on the Cumulant Generating Function of Dirichlet Processes