# Revisiting Spectral Representations in Generative Diffusion Models

arXiv: https://arxiv.org/abs/2609.08253 · HTML: https://mlsanity.com/paper/2609.08253/

## 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 63 of its 78 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Placed in

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

## Builds on (most cited first, 30 of 63)

- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [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)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Diffusion Autoencoders: Toward a Meaningful and Decodable Representation](https://mlsanity.com/paper/2111.15640/) (2021)

## Abstract (arXiv)

Diffusion models have shown remarkable performance on diverse generation tasks. Recent work finds that imposing representation alignment on the hidden states of diffusion networks can both facilitate training convergence and enhance sampling quality, yet the mechanism driving this synergy remains insufficiently understood. In this paper, we investigate the connection between self-supervised spectral representation learning and diffusion generative models through a shared perspective on perturbation kernels. On the diffusion side, samples (e.g., images, videos) are produced by reversing a stochastic noise-injection process specified by Gaussian kernels; on the spectral representation side, spectral embeddings emerge from contrasting positive and negative relations induced by random perturbation kernels. Motivated by this, we propose a self-supervised spectral representation alignment method to facilitate diffusion model training. In addition, we clarify how joint spectral learning can benefit diffusion training from a geometric perspective. Furthermore, we find that the optimization of the spectral alignment objective is in an equivalent form of diffusion score distillation in the representation space. Building on these findings, we integrate a spectral regularizer into diffusion training objectives to improve the performance of diffusion models on multiple datasets. Experiments across images and 3D point clouds show consistent gains in generation quality. Code is released at https://github.com/yuehaowang/spectral-reg-diffusion.