# S-Diff: An Anisotropic Diffusion Model for Collaborative Filtering in Spectral Domain

arXiv: https://arxiv.org/abs/2501.00384 · HTML: https://mlsanity.com/paper/2501.00384/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion recommenders, one of 14 directions in Diffusion models.
- Builds on 32 of its 49 references that are in the map.
- First posted on arXiv 31 Dec 2024.

## Placed in

- Diffusion models / [Diffusion recommenders](https://mlsanity.com/diffusion/diffusion-recommenders/)

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimation](https://mlsanity.com/paper/2106.05527/) (2021)
- [Diffusion Recommender Model](https://mlsanity.com/paper/2304.04971/) (2023)
- [Multiscale Structure Guided Diffusion for Image Deblurring](https://mlsanity.com/paper/2212.01789/) (2022)
- [Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion](https://mlsanity.com/paper/2310.20453/) (2023)
- [Diffusion Augmentation for Sequential Recommendation](https://mlsanity.com/paper/2309.12858/) (2023)
- [Blurring-Sharpening Process Models for Collaborative Filtering](https://mlsanity.com/paper/2211.09324/) (2022)
- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [DimeRec: A Unified Framework for Enhanced Sequential Recommendation via Generative Diffusion Models](https://mlsanity.com/paper/2408.12153/) (2024)
- [Collaborative Filtering Based on Diffusion Models: Unveiling the Potential of High-Order Connectivity](https://mlsanity.com/paper/2404.14240/) (2024)
- [A Generalized Neural Diffusion Framework on Graphs](https://mlsanity.com/paper/2312.08616/) (2023)
- [Revisiting Neighborhood-based Link Prediction for Collaborative Filtering](https://mlsanity.com/paper/2203.15789/) (2022)
- [Diffusion-based Negative Sampling on Graphs for Link Prediction](https://mlsanity.com/paper/2403.17259/) (2024)
- [A Directional Diffusion Graph Transformer for Recommendation](https://mlsanity.com/paper/2404.03326/) (2024)
- [Diffusion-based Contrastive Learning for Sequential Recommendation](https://mlsanity.com/paper/2405.09369/) (2024)
- [How Powerful is Graph Filtering for Recommendation](https://mlsanity.com/paper/2406.08827/) (2024)
- [RecFusion: A Binomial Diffusion Process for 1D Data for Recommendation](https://mlsanity.com/paper/2306.08947/) (2023)
- [PolyCF: Towards the Optimal Spectral Graph Filters for Collaborative Filtering](https://mlsanity.com/paper/2401.12590/) (2024)

## Built on by (most cited first, 6 of 6)

- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Fading to Grow: Growing Preference Ratios via Preference Fading Discrete Diffusion for Recommendation](https://mlsanity.com/paper/2509.26063/) (2025)
- [Eval4DiRec: A Unified and Systematic Evaluation Framework for Diffusion-based Recommender Systems](https://mlsanity.com/paper/2609.34404/) (2026)
- [Fine-Tuning Diffusion-Based Recommender Systems via Reinforcement Learning with Reward Function Optimization](https://mlsanity.com/paper/2511.06937/) (2025)
- [Towards A Tri-View Diffusion Framework for Recommendation](https://mlsanity.com/paper/2511.20122/) (2025)
- [Colored Graph Signal Diffusion Models](https://mlsanity.com/paper/2610.17282/) (2026)

## Abstract (arXiv)

Recovering user preferences from user-item interaction matrices is a key challenge in recommender systems. While diffusion models can sample and reconstruct preferences from latent distributions, they often fail to capture similar users' collective preferences effectively. Additionally, latent variables degrade into pure Gaussian noise during the forward process, lowering the signal-to-noise ratio, which in turn degrades performance. To address this, we propose S-Diff, inspired by graph-based collaborative filtering, better to utilize low-frequency components in the graph spectral domain. S-Diff maps user interaction vectors into the spectral domain and parameterizes diffusion noise to align with graph frequency. This anisotropic diffusion retains significant low-frequency components, preserving a high signal-to-noise ratio. S-Diff further employs a conditional denoising network to encode user interactions, recovering true preferences from noisy data. This method achieves strong results across multiple datasets.