Conditioning diffusion models by explicit forward-backward bridging
This provides a principled method for conditional simulation in diffusion models, addressing a key limitation for applications in generative modeling.
The paper tackles the problem of performing conditional simulation with unconditional diffusion models by formulating it as an inference problem on an augmented space, enabling exact conditional sampling without additional approximations beyond Monte Carlo error.
Given an unconditional diffusion model targeting a joint model $π(x, y)$, using it to perform conditional simulation $π(x \mid y)$ 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 $π(x \mid y)$. 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.