Deterministic Decomposition of Stochastic Generative Dynamics

2026-05-09

AI Summary

Existing stochastic generative models often conflate deterministic transport with diffusion-induced stochastic effects within a single velocity field, making it difficult to disentangle their respective contributions. This work proposes a natural transport–permeation decomposition that explicitly separates deterministic transport from diffusion-induced permeation in generative dynamics for the first time, and introduces a Bridge Matching framework to learn this decomposition. Built upon a flow-based architecture, the method integrates marginal and conditional modeling and leverages score function estimation to recover the permeation field, thereby enabling an interpretable decomposition of the velocity field. Experiments demonstrate that by modulating the weight of the permeation component, the sampling process can be flexibly controlled without compromising generation quality, significantly enhancing both interpretability and controllability of the model.

Abstract

Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field \(b_t\) of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects: \(b_t = u_t + d_t\), where \(u_t\) governs marginal probability transport and \(d_t\) captures an osmotic effect induced by diffusion and determined by the marginal score. Based on this decomposition, we propose Bridge Matching, a flow-based framework for learning decomposed generative dynamics through both marginal and conditional formulations. In generative modeling experiments, we recombine the learned components as \(b_t = u_t + λ_d d_t\), showing that the proposed decomposition enables interpretable and controllable sampling by adjusting the osmotic contribution in probability transport.

Problem

• stochastic generative dynamics
• deterministic velocity field
• transport decomposition
• osmotic effect
• diffusion

Innovation

• transport--osmotic decomposition
• stochastic generative dynamics
• Bridge Matching
• velocity-field parameterization
• score-based diffusion