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On the Equivalence of Optimal Transport Problem and Action Matching with Optimal Vector Fields
Nikita Kornilov, Alexander Korotin
Flow Matching (FM) method in generative modeling maps arbitrary probability distributions by constructing an interpolation between them and then learning the vector field that defi…
Sampling from Energy distributions with Target Concrete Score Identity
Sergei Kholkin, Francisco Vargas, Alexander Korotin
We introduce the Target Concrete Score Identity Sampler (TCSIS), a method for sampling from unnormalized densities on discrete state spaces by learning the reverse dynamics of a Co…
Time-Correlated Video Bridge Matching
Viacheslav Vasilev, Arseny Ivanov, Nikita Gushchin +2
Bridge Matching (BM) learns a stochastic transport between two data distributions and is therefore a natural tool for data-to-data tasks such as video frame interpolation, image-to…
Electric Currents for Discrete Data Generation
Alexander Kolesov, Stepan Manukhov, Vladimir V. Palyulin +1
We propose lectric urrent iscrete ata eneration (ECDG), a pioneering method for data generation in discrete settin…
Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport
Xavier Aramayo Carrasco, Grigoriy Ksenofontov, Aleksei Leonov +2
The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schrödinger bridge (SB) problem, play an important role in modern machine learning, linking generative…
Universal Inverse Distillation for Matching Models with Real-Data Supervision (No GANs)
Nikita Kornilov, David Li, Tikhon Mavrin +5
While achieving exceptional generative quality, modern diffusion, flow, and other matching models suffer from slow inference, as they require many steps of iterative generation. Re…
Overclocking Electrostatic Generative Models
Daniil Shlenskii, Alexander Korotin
Electrostatic generative models such as PFGM++ have recently emerged as a powerful framework, achieving competitive performance in image synthesis. PFGM++ operates in an extended d…
Exponential convergence rate for Iterative Markovian Fitting
Kirill Sokolov, Alexander Korotin
We consider the discrete-time Schrödinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullb…
Interaction Field Matching: Overcoming Limitations of Electrostatic Models
Stepan I. Manukhov, Alexander Kolesov, Vladimir V. Palyulin +1
Electrostatic field matching (EFM) has recently appeared as a novel physics-inspired paradigm for data generation and transfer using the idea of an electric capacitor. However, it…
Learning of Population Dynamics: Inverse Optimization Meets JKO Scheme
Mikhail Persiianov, Jiawei Chen, Petr Mokrov +3
Learning population dynamics involves recovering the underlying process that governs particle evolution, given evolutionary snapshots of samples at discrete time points. Recent met…
Risk-Averse Reinforcement Learning with Itakura-Saito Loss
Igor Udovichenko, Olivier Croissant, Anita Toleutaeva +2
Risk-averse reinforcement learning finds application in various high-stakes fields. Unlike classical reinforcement learning, which aims to maximize expected returns, risk-averse ag…
One-Step Residual Shifting Diffusion for Image Super-Resolution via Distillation
Daniil Selikhanovych, David Li, Aleksei Leonov +6
Diffusion models for super-resolution (SR) produce high-quality visual results but require expensive computational costs. Despite the development of several methods to accelerate d…
Field Matching: an Electrostatic Paradigm to Generate and Transfer Data
Alexander Kolesov, Manukhov Stepan, Vladimir V. Palyulin +1
We propose Electrostatic Field Matching (EFM), a novel method that is suitable for both generative modeling and distribution transfer tasks. Our approach is inspired by the physics…
Categorical Schrödinger Bridge Matching
Grigoriy Ksenofontov, Alexander Korotin
The Schrödinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data s…
InfoBridge: Mutual Information estimation via Bridge Matching
Sergei Kholkin, Ivan Butakov, Evgeny Burnaev +2
Diffusion bridge models have recently become a powerful tool in the field of generative modeling. In this work, we leverage their power to address another important problem in mach…
Inverse Bridge Matching Distillation
Nikita Gushchin, David Li, Daniil Selikhanovych +3
Learning diffusion bridge models is easy; making them fast and practical is an art. Diffusion bridge models (DBMs) are a promising extension of diffusion models for applications in…
A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers
Roman Tarasov, Petr Mokrov, Milena Gazdieva +2
Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain tran…