Supervised Guidance Training enables conditioning of infinite-dimensional diffusion models via an extended Doob h-transform so that fine-tuned models accurately sample from posteriors in function space.
That the time-reversal has a strong solution holds from Theorem 12 and Theorem 13 of Pidstrigach et al
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Supervised Guidance Training for Infinite-Dimensional Diffusion Models
Supervised Guidance Training enables conditioning of infinite-dimensional diffusion models via an extended Doob h-transform so that fine-tuned models accurately sample from posteriors in function space.