# Generalization Bound for Diffusion Models using Random Features

arXiv: https://arxiv.org/abs/2310.04417 · HTML: https://mlsanity.com/paper/2310.04417/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 6 Oct 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Variational Autoencoder for Deep Learning of Images, Labels and Captions](https://mlsanity.com/paper/1609.08976/) (2016)
- [Generative Modeling with Denoising Auto-Encoders and Langevin Sampling](https://mlsanity.com/paper/2002.00107/) (2020)
- [Adversarial score matching and improved sampling for image generation](https://mlsanity.com/paper/2009.05475/) (2020)
- [Diffusion Normalizing Flow](https://mlsanity.com/paper/2110.07579/) (2021)
- [Generating High Fidelity Images with Subscale Pixel Networks and Multidimensional Upscaling](https://mlsanity.com/paper/1812.01608/) (2018)
- [Hybrid Random Features](https://mlsanity.com/paper/2110.04367/) (2021)
- [HARFE: Hard-Ridge Random Feature Expansion](https://mlsanity.com/paper/2202.02877/) (2022)
- [SRMD: Sparse Random Mode Decomposition](https://mlsanity.com/paper/2204.06108/) (2022)
- [SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemics](https://mlsanity.com/paper/2211.08277/) (2022)
- [Deep Semi-Random Features for Nonlinear Function Approximation](https://mlsanity.com/paper/1702.08882/) (2017)

## Built on by (most cited first, 3 of 3)

- [Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves](https://mlsanity.com/paper/2502.00336/) (2025)
- [Dispersion based Recurrent Neural Network Model for Methane Monitoring in Albertan Tailings Ponds](https://mlsanity.com/paper/2411.06741/) (2024)
- [Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Data](https://mlsanity.com/paper/2603.22962/) (2026)

## Abstract (arXiv)

Diffusion probabilistic models have been successfully used to generate data from noise. However, most diffusion models are computationally expensive and difficult to interpret with a lack of theoretical justification. Random feature models on the other hand have gained popularity due to their interpretability but their application to complex machine learning tasks remains limited. In this work, we present a diffusion model-inspired deep random feature model that is interpretable and gives comparable numerical results to a fully connected neural network having the same number of trainable parameters. Specifically, we extend existing results for random features and derive generalization bounds between the distribution of sampled data and the true distribution using properties of score matching. We validate our findings by generating samples on the fashion MNIST dataset and instrumental audio data.