Research map / Image generation / Fast diffusion sampling
Shallow diffusion networks provably learn hidden low-dimensional structure
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Shows that diffusion models with shallow ReLU networks (Barron space F_1) adapt to linear-subspace and independent-component latent structure, giving end-to-end sample complexity bounds that scale with latent dimension rather than ambient dimension.
Problem
Learning diffusion models (score estimation plus sampling) for data concentrated on low-dimensional latent structure suffers from the curse of dimensionality in the ambient dimension, and prior guarantees needed latent-aware architectures or sparsity constraints.
Approach
Use the Barron space F_1 of infinite-width shallow ReLU networks as the score function class; the low-index structure of F_1 lets the score of subspace or independent-component distributions be approximated with F_1 norm that does not depend exponentially on ambient dimension, yielding score-matching and sampling bounds depending on latent dimension.
Key results
- Score-estimation risk for F_1-constrained ERM scales as n^{-2/(d+5)} with latent dimension d replacing ambient D (up to poly(D) prefactors).
- End-to-end KL bound eps^2 requires n on the order of poly(D) * eps^{-(d+5)} samples for the subspace setting, without latent-aware architectures.
- Extension to independent components gives sum over components of (K/n)^{2/(d_i+5)} risk scaling.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| learn score functions with shallow Barron networks without latent-dimension knowledge or sparsity constraints | Diffusion models for low-dimensional subspace data · Latent subspace | sample complexity dependence on dimension | Helped |
| learn score functions with shallow Barron networks | Diffusion models for independent-component data · Latent independent components | score estimation error dependence on dimension | Helped |
Limitations
- Sample complexity carries poly(D) prefactors that the authors leave open to remove.
- Rate n^{2/(d+5)} is not matching the minimax n^{2/(d+4)} rate.
- Analysis covers only linear subspace and independent-component structure, not nonlinear manifolds; whitening step for non-orthogonal components leaves estimation error unanalyzed.
Experimental setup
Metrics: L2 score error KL divergence bound sample complexity exponent
Baselines: Oko et al. (latent subspace-aware diffusion bound) minimax score matching rate n^{-2/(D+4)}
Builds on: Barron space / F_1 norm denoising score matching exponential integrator sampler Oko et al. latent subspace diffusion analysis
Closest papers by meaning
- A solvable model of learning generative diffusion: theory and insights (NeurIPS 2025 · similarity 0.89)
- Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models (NeurIPS 2024 · similarity 0.89)
- Nonparametric Estimation of a Factorizable Density using Diffusion Models (NeurIPS 2026 · similarity 0.89)
- Neural Diffusion Models (ICML 2024 · similarity 0.88)
- Generalization in diffusion models arises from geometry-adaptive harmonic representations (ICLR 2024 · similarity 0.88)
- Structure-Guided Adversarial Training of Diffusion Models (CVPR 2024 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.