mlsanityData to 14 Oct 2026

Latent Nonlinear Denoising Score Matching for Enhanced Learning of Structured Distributions

arXiv 2512.06615 ↗First posted 7 Dec 2025stat.ML cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We present latent nonlinear denoising score matching (LNDSM), a novel training objective for score-based generative models that integrates nonlinear forward dynamics with the VAE-based latent SGM framework. This combination is achieved by reformulating the cross-entropy term using the approximate Gaussian transition induced by the Euler-Maruyama scheme. To ensure numerical stability, we identify and remove two zero-mean but variance exploding terms arising from small time steps. Experiments on variants of the MNIST dataset demonstrate that the proposed method achieves faster synthesis and enhanced learning of inherently structured distributions. Compared to benchmark structure-agnostic latent SGMs, LNDSM consistently attains superior sample quality and variability.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 16 of its 24 references that are in the map. First posted on arXiv 7 Dec 2025.

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16 of 24 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Nonlinear denoising score matching for enhanced learning of structured distributions24 May
  2. 2024Structure Preserving Diffusion Models29 Feb
  3. 2021Score-based Generative Modeling in Latent Space10 Jun
  4. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 10

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2022Generative Adversarial Networkscited by 5,627
  3. 2017Squeeze-and-Excitation Networkscited by 4,789
  4. 2016Improved Techniques for Training GANscited by 2,970
  5. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,476
  6. 2015Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)cited by 1,070
  7. 2020NVAE: A Deep Hierarchical Variational Autoencodercited by 637
  8. 2022Brain Imaging Generation with Latent Diffusion Modelscited by 268
  9. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 186
  10. 2020Group Equivariant Generative Adversarial Networkscited by 19

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  3. 2026Non-asymptotic Convergence of Stochastic Gradient Descent in Score-based Generative Models
  4. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion
  5. 2025Implicit score matching meets denoising score matching: improved rates of convergence and log-density Hessian estimation
  6. 2022From Denoising Diffusions to Denoising Markov Models
  7. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
  8. 2026Taming Score-Based Denoisers in ADMM: A Convergent Plug-and-Play Framework