This work uses causal optimal transport to define loss functions that identify a minimum-entropy control for guidance under minimal assumptions in conditioned generative models.
Abstract
Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, \`a la \"Ust\"unel.
We study generative bootstrap processes obtained by resampling from fitted generative distributions. We establish necessary and sufficient conditions for their conditional weak convergence to the $P$-Brownian bridge, formulated in terms of finite-dimensional conditional weak convergence and conditional asymptotic equic...
Optimal Transport Dropout (OTD) is introduced, which offers a way to learn structured predictive uncertainty without explicit posterior inference or ensembles of independently trained predictors.
Giacomo Lorenzon, Francesco Regazzoni· 0 citations
A conditioning mechanism for diffusion models based on multi-speed joint diffusion of the target and the condition learns an unconditional joint score network and enforces conditioning at inference via a plug-in correction term, and derives explicit conditional reverse-time SDEs and approximate probability-flow ODEs.
Libo Chen, Souvik Ghosh, Teo Deveney et al.· 0 citations
Simplex Diffusion Models (SDMs) are proposed, a framework that lifts the diffusion process to the probability simplex to represent beliefs over categories and can carry uncertainty across denoising steps, which mitigates information collapse.
Justin Deschenaux, Alexandre Galashov, Andrew Campbell et al.· 1 citation
A framework for designing the reference process that achieves tractable time-dependent conditional distributions and then construct the reference process realizing them as its marginals is proposed, revealing that score matching is not fundamental to diffusion-model training but instead emerges naturally through revers...
Simplax is introduced, an exact Dirichlet--categorical augmentation that couples each corrupted categorical state with an auxiliary simplex-valued variable while preserving the original uniform diffusion process as its categorical marginal.
Jinya Sakurai, Patrick Pynadath, Satoshi Hayakawa et al.· 1 citation
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