# Escaping the Euclidean Void: Manifold-Informed Flow Matching for Sequential Recommendation

arXiv: https://arxiv.org/abs/2607.23762 · HTML: https://mlsanity.com/paper/2607.23762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion recommenders, one of 14 directions in Diffusion models.
- Builds on 35 of its 49 references that are in the map.
- First posted on arXiv 26 Jul 2026.

## Placed in

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

## Builds on (most cited first, 30 of 35)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Self-Attentive Sequential Recommendation](https://mlsanity.com/paper/1808.09781/) (2018)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer](https://mlsanity.com/paper/1904.06690/) (2019)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Personalized Top-N Sequential Recommendation via Convolutional Sequence Embedding](https://mlsanity.com/paper/1809.07426/) (2018)
- [Session-based Recommendation with Graph Neural Networks](https://mlsanity.com/paper/1811.00855/) (2018)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Contrastive Learning for Representation Degeneration Problem in Sequential Recommendation](https://mlsanity.com/paper/2110.05730/) (2021)
- [A Simple Convolutional Generative Network for Next Item Recommendation](https://mlsanity.com/paper/1808.05163/) (2018)
- [Hierarchical Gating Networks for Sequential Recommendation](https://mlsanity.com/paper/1906.09217/) (2019)
- [DiffuRec: A Diffusion Model for Sequential Recommendation](https://mlsanity.com/paper/2304.00686/) (2023)
- [Global Context Enhanced Graph Neural Networks for Session-based Recommendation](https://mlsanity.com/paper/2106.05081/) (2021)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion](https://mlsanity.com/paper/2310.20453/) (2023)
- [Item2Vec: Neural Item Embedding for Collaborative Filtering](https://mlsanity.com/paper/1603.04259/) (2016)
- [Translation-based Recommendation](https://mlsanity.com/paper/1707.02410/) (2017)
- [Plug-in Diffusion Model for Sequential Recommendation](https://mlsanity.com/paper/2401.02913/) (2024)
- [Graph Masked Autoencoder for Sequential Recommendation](https://mlsanity.com/paper/2305.04619/) (2023)
- [MELT: Mutual Enhancement of Long-Tailed User and Item for Sequential Recommendation](https://mlsanity.com/paper/2304.08382/) (2023)
- [AutoSeqRec: Autoencoder for Efficient Sequential Recommendation](https://mlsanity.com/paper/2308.06878/) (2023)
- [Distinguished Quantized Guidance for Diffusion-based Sequence Recommendation](https://mlsanity.com/paper/2501.17670/) (2025)
- [Diffusion-Based Cloud-Edge-Device Collaborative Learning for Next POI Recommendations](https://mlsanity.com/paper/2405.13811/) (2024)
- [Flow Matching for Collaborative Filtering](https://mlsanity.com/paper/2502.07303/) (2025)
- [Graph and Sequential Neural Networks in Session-based Recommendation: A Survey](https://mlsanity.com/paper/2408.14851/) (2024)

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

- [Graph-Spectral Flow Matching for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2609.36765/) (2026)

## Abstract (arXiv)

Conventional recommenders capture users' preferences by optimizing observed user-item relations, whereas continuous generative recommendation additionally learns the trajectory of synthesizing a target item. Flow matching drives this process by gradually shaping initial noise into a definitive next-item representation through intermediate states in a continuous embedding space. However, item catalogs are discrete and sparsely supported, meaning even a straight Euclidean path can cross continuous regions that contain little evidence of valid item semantics. Formalizing this failure as the Euclidean void, we propose MIRAGE, a Manifold-Informed Rectification framework for Accelerated Generation of Embeddings in sequential recommendation, which rectifies the learned embedding geometry around an unchanged straight probability path. By leveraging an item co-occurrence graph as a proxy for the underlying semantic manifold, MIRAGE aligns interpolated path states with local anchors, reorganizing the embedding space to ground the trajectory in valid item support. MIRAGE retains the original probability path and uses the graph only during training, thereby enabling accurate and efficient one-step inference. Extensive experiments on four real-world datasets reveal that MIRAGE consistently outperforms state-of-the-art baselines, effectively boosting performance on sparsely observed targets while achieving robust overall accuracy. Our code will be made publicly available upon publication.