# Spectral Regularization for Diffusion Models

arXiv: https://arxiv.org/abs/2603.02447 · HTML: https://mlsanity.com/paper/2603.02447/

## Key facts

- Cited by 1 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 2 Mar 2026.

## 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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Wavelet-based Fourier Information Interaction with Frequency Diffusion Adjustment for Underwater Image Restoration](https://mlsanity.com/paper/2311.16845/) (2023)
- [Generative Diffusion Models on Graphs: Methods and Applications](https://mlsanity.com/paper/2302.02591/) (2023)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [Patched Denoising Diffusion Models For High-Resolution Image Synthesis](https://mlsanity.com/paper/2308.01316/) (2023)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulation](https://mlsanity.com/paper/2302.00190/) (2023)
- [Spectral Analysis of Diffusion Models with Application to Schedule Design](https://mlsanity.com/paper/2502.00180/) (2025)
- [PhysioWave: A Multi-Scale Wavelet-Transformer for Physiological Signal Representation](https://mlsanity.com/paper/2506.10351/) (2025)
- [Shaping Inductive Bias in Diffusion Models through Frequency-Based Noise Control](https://mlsanity.com/paper/2502.10236/) (2025)
- [A Hybrid Wavelet-Fourier Method for Next-Generation Conditional Diffusion Models](https://mlsanity.com/paper/2504.03821/) (2025)
- [Wavelet Fourier Diffuser: Frequency-Aware Diffusion Model for Reinforcement Learning](https://mlsanity.com/paper/2509.19305/) (2025)

## Built on by (most cited first, 1 of 1)

- [Flicker-DDPM: Accelerating Denoising Diffusion via 1/f Colored Noise Injection](https://mlsanity.com/paper/2606.03393/) (2026)

## Abstract (arXiv)

Diffusion models are typically trained using pointwise reconstruction objectives that are agnostic to the spectral and multi-scale structure of natural signals. We propose a loss-level spectral regularization framework that augments standard diffusion training with differentiable Fourier- and wavelet-domain losses, without modifying the diffusion process, model architecture, or sampling procedure. The proposed regularizers act as soft inductive biases that encourage appropriate frequency balance and coherent multi-scale structure in generated samples. Our approach is compatible with DDPM, DDIM, and EDM formulations and introduces negligible computational overhead. Experiments on image and audio generation demonstrate consistent improvements in sample quality, with the largest gains observed on higher-resolution, unconditional datasets where fine-scale structure is most challenging to model.