Universality of Gaussian-Mixture Reverse Kernels in Conditional Diffusion
We prove that conditional diffusion models whose reverse kernels are finite Gaussian mixtures with ReLU-network logits can approximate suitably regular target distributions arbitrarily well in context-averaged conditional KL divergence, up to an irreducible terminal mismatch that typically vanishes with increasing diffusion horizon. A path-space decomposition reduces the output error to this mismatch plus per-step reverse-kernel errors; assuming each reverse kernel factors through a finite-dimensional feature map, each step becomes a static conditional density approximation problem, solved by composing Norets' Gaussian-mixture theory with quantitative ReLU bounds. Under exact terminal mat...
| Authors | Nafiz Ishtiaque, Syed Arefinul Haque, Kazi Ashraful Alam et al. |
|---|---|
| Primary category | cs.LG |
| Published | 15 April 2026 |
| Last updated at source | 15 April 2026 |
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