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ccrdallas t1_iuimqp9 wrote

Diffusion models essentially use a stochastic differential equation to produce samples. An MCMC method that produces samples using such equations, often known as Langevin diffusions, are called the Unadjusted/Metropolis-Adjusted Langevin algorithm(s).

Typically we don’t use the metropolis adjustment in practice and so these methods aren’t truly Metropolis-Hastings algorithms, they are just discretized SDEs. The purpose of the adjustment is to reduce bias and ensure convergence to a particular distribution but these are lesser concerns in diffusion models, particularly with small enough step size.

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Red-Portal t1_iuipcuj wrote

>are lesser concerns in diffusion models

Lesser concern because we don't care about the bias that much as long as the samples look okay. However small the step size, the bias will be there. Actually, unadjusted Langevin is pretty terrible for statistical applications in terms of bias even with small stepsizes.

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ZeronixSama OP t1_iuiqs8u wrote

I see, so in other words: in diffusion models there is no rejection sampling step that the Metropolis-Hastings algorithm would usually do.

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