Abstract: Diffusion model is a prevailing Generative AI approach. It uses a score function to characterize a complex data distribution and its evolution toward an easy distribution. This talk will report progress in two different topics, both closely related to the origins of the score function.
The first topic, which will take most time of the talk, will be on a quantification of the generation accuracy of diffusion model. The importance of this problem already led to a rich and substantial literature; however, most existing theoretical investigations assumed that an epsilon-accurate score function has already been oracle-given, and focused on just the inference process of diffusion model. I will instead describe a first quantitative understanding of the actual generative modeling protocol, including both score training (optimization) and inference (sampling). The resulting full error analysis will elucidate (again, but this time theoretically) how to design the training and inference processes for effective generation.
The second topic will no longer be about generative modeling, but sampling instead. The goal is leverage the fact that diffusion model is very good at handling multimodal distributions, and extrapolate it to the holy grail problem of efficient sampling from multimodal density. There, one needs to rethink about how to get the score function, as no more data samples are available and one instead has unnormalized density. A new sampler that is insensitive to metastability, with performance guarantee, and not even requiring continuous density, will be presented.
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