Conditioning diffusion models by explicit forward-backward bridging

TL;DR

This paper introduces a novel method for exact conditional simulation using diffusion models by framing it as an inference problem on an augmented space, enabling efficient sampling without additional model approximation.

Contribution

It presents a new perspective on conditional diffusion modeling via partial SDE bridges, allowing exact conditional sampling with particle Gibbs and pseudo-marginal methods.

Findings

Efficient conditional sampling without extra model approximation.

Applicable to synthetic and real data examples.

Provides a principled inference framework for diffusion models.

Abstract

Given an unconditional diffusion model targeting a joint model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the denoising SDE after the fact. In this work, we express \emph{exact} conditional simulation within the \emph{approximate} diffusion model as an inference problem on an augmented space corresponding to a partial SDE bridge. This perspective allows us to implement efficient and principled particle Gibbs and pseudo-marginal samplers marginally targeting the conditional distribution $\pi(x \mid y)$. Contrary to existing methodology, our methods do not introduce any additional approximation to the unconditional diffusion model aside from the Monte Carlo error. We showcase the benefits and drawbacks of our approach on a series of synthetic and real data examples.