# Hyperbolic Diffusion Recommender Model

arXiv: https://arxiv.org/abs/2504.01541 · HTML: https://mlsanity.com/paper/2504.01541/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 81 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 30 of 48)

- [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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Label-Efficient Semantic Segmentation with Diffusion Models](https://mlsanity.com/paper/2112.03126/) (2021)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023)
- [Learning Disentangled Representations for Recommendation](https://mlsanity.com/paper/1910.14238/) (2019)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [DiffuRec: A Diffusion Model for Sequential Recommendation](https://mlsanity.com/paper/2304.00686/) (2023)
- [Diffusion Recommender Model](https://mlsanity.com/paper/2304.04971/) (2023)
- [Denoising Implicit Feedback for Recommendation](https://mlsanity.com/paper/2006.04153/) (2020)
- [IRGAN: A Minimax Game for Unifying Generative and Discriminative Information Retrieval Models](https://mlsanity.com/paper/1705.10513/) (2017)
- [A Neural Influence Diffusion Model for Social Recommendation](https://mlsanity.com/paper/1904.10322/) (2019)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Point Cloud Pre-training with Diffusion Models](https://mlsanity.com/paper/2311.14960/) (2023)
- [DiffNet++: A Neural Influence and Interest Diffusion Network for Social Recommendation](https://mlsanity.com/paper/2002.00844/) (2020)
- [DiffKG: Knowledge Graph Diffusion Model for Recommendation](https://mlsanity.com/paper/2312.16890/) (2023)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [Diffusion Augmentation for Sequential Recommendation](https://mlsanity.com/paper/2309.12858/) (2023)
- [Multimodal Recommender Systems: A Survey](https://mlsanity.com/paper/2302.03883/) (2023)

## Built on by (most cited first, 9 of 9)

- [Real-Time Aligned Reward Model beyond Semantics](https://mlsanity.com/paper/2601.22664/) (2026)
- [Contextual Rollout Bandits for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2602.08499/) (2026)
- [Masked Diffusion for Generative Recommendation](https://mlsanity.com/paper/2511.23021/) (2025)
- [FCKT: Fine-Grained Cross-Task Knowledge Transfer with Semantic Contrastive Learning for Targeted Sentiment Analysis](https://mlsanity.com/paper/2505.21040/) (2025)
- [Learning Adaptive Distribution Alignment with Neural Characteristic Function for Graph Domain Adaptation](https://mlsanity.com/paper/2602.10489/) (2026)
- [SynGR: Unleashing the Potential of Cross-Modal Synergy for Generative Recommendation](https://mlsanity.com/paper/2605.18920/) (2026)
- [Semantic Granularity Navigation in Image Editing](https://mlsanity.com/paper/2605.21190/) (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)

## Abstract (arXiv)

Diffusion models (DMs) have emerged as the new state-of-the-art family of deep generative models. To gain deeper insights into the limitations of diffusion models in recommender systems, we investigate the fundamental structural disparities between images and items. Consequently, items often exhibit distinct anisotropic and directional structures that are less prevalent in images. However, the traditional forward diffusion process continuously adds isotropic Gaussian noise, causing anisotropic signals to degrade into noise, which impairs the semantically meaningful representations in recommender systems. Inspired by the advancements in hyperbolic spaces, we propose a novel textitHyperbolic textitDiffusion textitRecommender textitModel (named HDRM). Unlike existing directional diffusion methods based on Euclidean space, the intrinsic non-Euclidean structure of hyperbolic space makes it particularly well-adapted for handling anisotropic diffusion processes. In particular, we begin by formulating concepts to characterize latent directed diffusion processes within a geometrically grounded hyperbolic space. Subsequently, we propose a novel hyperbolic latent diffusion process specifically tailored for users and items. Drawing upon the natural geometric attributes of hyperbolic spaces, we impose structural restrictions on the space to enhance hyperbolic diffusion propagation, thereby ensuring the preservation of the intrinsic topology of user-item graphs. Extensive experiments on three benchmark datasets demonstrate the effectiveness of HDRM.