Control Consistency Losses for Diffusion Bridges

TL;DR

This paper introduces a new method for learning diffusion bridges using a self-consistency property of optimal control, improving simulation of conditioned diffusion processes especially for rare events.

Contribution

It proposes an iterative online algorithm that learns conditioned dynamics without differentiating through trajectories, connecting self-consistency with stochastic optimal control.

Findings

The method performs well across various empirical scenarios.

It does not require differentiation through simulated trajectories.

The approach is applicable to rare event simulation in diffusion processes.

Abstract

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we propose a novel approach for learning diffusion bridges based on a self-consistency property of the optimal control. The resulting algorithm learns the conditioned dynamics in an iterative online manner, and exhibits strong performance in a range of empirical settings without requiring differentiation through simulated trajectories. Beyond the diffusion bridge setting, we draw connections between our self-consistency framework and recent advances in the wider stochastic optimal control literature.