The paper introduces a new method for conditioning degenerate diffusion models, which are generative models that rely on diffusion processes with singular diffusion coefficients. Traditional approaches use score functions for guidance, but this work employs causal optimal transport to define approximate loss functions that can identify a minimum‑entropy control even when conditional densities are non‑existent or non‑smooth. The method hinges on the predictable representation property of conditioned diffusion processes and the well‑posedness of their martingale problem, following the framework of "Ust"unel.
By U\u{g}ur Ayd{\i}n, Tamer Ba\c{s}ar
arXiv:2602. 05533v3 Announce Type: replace Abstract: We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one.
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