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arXiv Statistics ML By Kaichen Shen, Wei Zhu

Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions

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The paper introduces Latent Nonlinear Denoising Score Matching (LNDSM), a method that integrates nonlinear, structure-informed latent diffusions with a variational autoencoder framework. LNDSM designs the forward diffusion to admit a chosen reference distribution, such as a Gaussian mixture, and derives a computable approximation to a cross‑entropy upper bound using Euler‑Maruyama discretization. Experiments on benchmark image datasets show that LNDSM improves sample quality, mode balance, and training efficiency compared to conventional latent score‑based generative models.

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