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Diffusion Schrodinger Bridges for Bayesian Computation
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DOI：10.1214/23-STS908.png)
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Abstract
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Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more generally, any target distribution whose density is known up to a normalizing constant. The key idea is to consider a forward noising diffusion initialized at the target distribution, which transports this latter to a normal distribution for long diffusion times. The time reversal of this process, the denoising diffusion, thus transports the normal distribution to the target distribution and can be approximated so as to sample from the target. To accelerate simulation, we show how one can introduce and approximate a Schrodinger bridge between these two distributions, that is, a diffusion which transports the normal to the target in finite time.
Keywords:
Optimal transport
Schrodinger bridge
score matching
stochastic differential equation
time reversal
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