# Graph Signal Diffusion Model for Collaborative Filtering

arXiv: https://arxiv.org/abs/2311.08744 · HTML: https://mlsanity.com/paper/2311.08744/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion recommenders, one of 14 directions in Diffusion models.
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [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)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Learning Disentangled Representations for Recommendation](https://mlsanity.com/paper/1910.14238/) (2019)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [DiffuRec: A Diffusion Model for Sequential Recommendation](https://mlsanity.com/paper/2304.00686/) (2023)
- [Diffusion Recommender Model](https://mlsanity.com/paper/2304.04971/) (2023)
- [IRGAN: A Minimax Game for Unifying Generative and Discriminative Information Retrieval Models](https://mlsanity.com/paper/1705.10513/) (2017)
- [Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion](https://mlsanity.com/paper/2310.20453/) (2023)
- [Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition](https://mlsanity.com/paper/1504.05477/) (2015)
- [Graph Trend Filtering Networks for Recommendations](https://mlsanity.com/paper/2108.05552/) (2021)
- [How Powerful is Graph Convolution for Recommendation?](https://mlsanity.com/paper/2108.07567/) (2021)
- [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)
- [Conditional Denoising Diffusion for Sequential Recommendation](https://mlsanity.com/paper/2304.11433/) (2023)
- [Discrete Conditional Diffusion for Reranking in Recommendation](https://mlsanity.com/paper/2308.06982/) (2023)
- [Revisiting Neighborhood-based Link Prediction for Collaborative Filtering](https://mlsanity.com/paper/2203.15789/) (2022)
- [LD4MRec: Simplifying and Powering Diffusion Model for Multimedia Recommendation](https://mlsanity.com/paper/2309.15363/) (2023)

## Built on by (most cited first, 25 of 25)

- [Score-based Generative Diffusion Models for Social Recommendations](https://mlsanity.com/paper/2412.15579/) (2024)
- [A Survey on Diffusion Models for Recommender Systems](https://mlsanity.com/paper/2409.05033/) (2024)
- [Preference Diffusion for Recommendation](https://mlsanity.com/paper/2410.13117/) (2024)
- [Flow Matching for Collaborative Filtering](https://mlsanity.com/paper/2502.07303/) (2025)
- [Graph-Aware Diffusion for Signal Generation](https://mlsanity.com/paper/2510.05036/) (2025)
- [Graph Spectral Filtering with Chebyshev Interpolation for Recommendation](https://mlsanity.com/paper/2505.00552/) (2025)
- [Masked Diffusion for Generative Recommendation](https://mlsanity.com/paper/2511.23021/) (2025)
- [Graph Signal Generative Diffusion Models](https://mlsanity.com/paper/2509.17250/) (2025)
- [Addressing Missing Data Issue for Diffusion-based Recommendation](https://mlsanity.com/paper/2505.12283/) (2025)
- [Diffusion Models in Recommendation Systems: A Survey](https://mlsanity.com/paper/2501.10548/) (2025)
- [Unleashing the Potential of Two-Tower Models: Diffusion-Based Cross-Interaction for Large-Scale Matching](https://mlsanity.com/paper/2502.20687/) (2025)
- [Continuous-time Discrete-space Diffusion Model for Recommendation](https://mlsanity.com/paper/2511.12114/) (2025)
- [Stability of Flow Models for Graph Signals](https://mlsanity.com/paper/2607.07510/) (2026)
- [Diffusion-augmented Graph Contrastive Learning for Collaborative Filter](https://mlsanity.com/paper/2503.16290/) (2025)
- [Rethinking Popularity Bias in Collaborative Filtering via Analytical Vector Decomposition](https://mlsanity.com/paper/2512.10688/) (2025)
- [MCLMR: A Model-Agnostic Causal Learning Framework for Multi-Behavior Recommendation](https://mlsanity.com/paper/2603.25126/) (2026)
- [FAVE: Flow-based Average Velocity Establishment for Sequential Recommendation](https://mlsanity.com/paper/2604.04427/) (2026)
- [Eval4DiRec: A Unified and Systematic Evaluation Framework for Diffusion-based Recommender Systems](https://mlsanity.com/paper/2609.34404/) (2026)
- [Beyond Interactions: Node-Level Graph Generation for Knowledge-Free Augmentation in Recommender Systems](https://mlsanity.com/paper/2507.20578/) (2025)
- [Fine-Tuning Diffusion-Based Recommender Systems via Reinforcement Learning with Reward Function Optimization](https://mlsanity.com/paper/2511.06937/) (2025)
- [Enhancing Conversational Recommender Systems with Tree-Structured Knowledge and Pretrained Language Models](https://mlsanity.com/paper/2511.12579/) (2025)
- [Towards A Tri-View Diffusion Framework for Recommendation](https://mlsanity.com/paper/2511.20122/) (2025)
- [MealRec: Multi-granularity Sequential Modeling via Hierarchical Diffusion Models for Micro-Video Recommendation](https://mlsanity.com/paper/2603.01926/) (2026)
- [Diffusion Language Model for Recommendation](https://mlsanity.com/paper/2607.21519/) (2026)
- [Stable Filters for Generative Modeling of Graph Signals](https://mlsanity.com/paper/2609.18759/) (2026)

## Abstract (arXiv)

Collaborative filtering is a critical technique in recommender systems. It has been increasingly viewed as a conditional generative task for user feedback data, where newly developed diffusion model shows great potential. However, existing studies on diffusion model lack effective solutions for modeling implicit feedback. Particularly, the standard isotropic diffusion process overlooks correlation between items, misaligned with the graphical structure of the interaction space. Meanwhile, Gaussian noise destroys personalized information in a user's interaction vector, causing difficulty in its reconstruction. In this paper, we adapt standard diffusion model and propose a novel Graph Signal Diffusion Model for Collaborative Filtering (named GiffCF). To better represent the correlated distribution of user-item interactions, we define a generalized diffusion process using heat equation on the item-item similarity graph. Our forward process smooths interaction signals with an advanced family of graph filters, introducing the graph adjacency as beneficial prior knowledge for recommendation. Our reverse process iteratively refines and sharpens latent signals in a noise-free manner, where the updates are conditioned on the user's history and computed from a carefully designed two-stage denoiser, leading to high-quality reconstruction. Finally, through extensive experiments, we show that GiffCF effectively leverages the advantages of both diffusion model and graph signal processing, and achieves state-of-the-art performance on three benchmark datasets.