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- SS is an improved version of GD that can generate trajectories closer to user input while maintaining the original motion constraints. Repeating each guided diffusion step M steps by adding back noise in a MCMC style effectively samples the correct gradients (direct adding denoising and alignment gradients in GD is in fact mathematically incorrect) of the composed distribution (original policy distribution composed with inference-time user objectives). + SS is an improved version of GD that can generate trajectories closer to user input while maintaining the original motion constraints. Repeating each guided diffusion step M steps by adding back noise in a MCMC style effectively samples the correct gradients (direct adding denoising and alignment gradients in GD is in fact mathematically incorrect) of the composed distribution (original policy distribution composed with inference-time user objectives).
+ + Consider the toy example of composing a pre-trained policy distribution with an inference-time point input. The goal is to sample an in-distribution (highly likely) data point with respect to the pre-trained distribution while maximizing alignment with the constructed point objective distribution. GD approximately samples from the sum distribution, which can result in OOD samples that violate likelihood constraints learned by the pre-trained distribution. In contrast, SS approximately samples from the product distribution via Annealed MCMC. See below for videos of Langevin sampling with combined denoising and alignment gradients in GD and SS. +
Unconditional sampling a pre-trained distribution
Conditional sampling with GD
Conditional sampling with SS
Denoising Evolution under BI
Denoising evolution under BI
Denoising Evolution under GD
Denoising evolution under GD
Denoising Evolution under SS
Denoising evolution under SS