# FAVE: Flow-based Average Velocity Establishment for Sequential Recommendation

arXiv: https://arxiv.org/abs/2604.04427 · HTML: https://mlsanity.com/paper/2604.04427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 6 Apr 2026.

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

- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Session-based Recommendations with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06939/) (2015)
- [Personalized Top-N Sequential Recommendation via Convolutional Sequence Embedding](https://mlsanity.com/paper/1809.07426/) (2018)
- [Recommender Systems with Generative Retrieval](https://mlsanity.com/paper/2305.05065/) (2023)
- [Contrastive Learning for Representation Degeneration Problem in Sequential Recommendation](https://mlsanity.com/paper/2110.05730/) (2021)
- [DiffuRec: A Diffusion Model for Sequential Recommendation](https://mlsanity.com/paper/2304.00686/) (2023)
- [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)
- [Fisher Flow Matching for Generative Modeling over Discrete Data](https://mlsanity.com/paper/2405.14664/) (2024)
- [Translation-based Recommendation](https://mlsanity.com/paper/1707.02410/) (2017)
- [DiffKG: Knowledge Graph Diffusion Model for Recommendation](https://mlsanity.com/paper/2312.16890/) (2023)
- [Diffusion Models for Generative Outfit Recommendation](https://mlsanity.com/paper/2402.17279/) (2024)
- [Denoising Diffusion Recommender Model](https://mlsanity.com/paper/2401.06982/) (2024)
- [IISAN: Efficiently Adapting Multimodal Representation for Sequential Recommendation with Decoupled PEFT](https://mlsanity.com/paper/2404.02059/) (2024)
- [Graph Signal Diffusion Model for Collaborative Filtering](https://mlsanity.com/paper/2311.08744/) (2023)
- [Discrete Conditional Diffusion for Reranking in Recommendation](https://mlsanity.com/paper/2308.06982/) (2023)
- [Step-by-Step Diffusion: An Elementary Tutorial](https://mlsanity.com/paper/2406.08929/) (2024)
- [AutoSeqRec: Autoencoder for Efficient Sequential Recommendation](https://mlsanity.com/paper/2308.06878/) (2023)
- [Generative Next POI Recommendation with Semantic ID](https://mlsanity.com/paper/2506.01375/) (2025)
- [Learning Graph ODE for Continuous-Time Sequential Recommendation](https://mlsanity.com/paper/2304.07042/) (2023)
- [Preference Alignment with Flow Matching](https://mlsanity.com/paper/2405.19806/) (2024)
- [Flow Matching for Collaborative Filtering](https://mlsanity.com/paper/2502.07303/) (2025)
- [Unlocking the Power of Diffusion Models in Sequential Recommendation: A Simple and Effective Approach](https://mlsanity.com/paper/2505.19544/) (2025)
- [FlowRec: Prior-Informed Flow Matching for Efficient Sequential Recommendation Generation](https://mlsanity.com/paper/2508.17618/) (2025)
- [Towards Distribution Matching between Collaborative and Language Spaces for Generative Recommendation](https://mlsanity.com/paper/2504.07363/) (2025)

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

- [Escaping the Euclidean Void: Manifold-Informed Flow Matching for Sequential Recommendation](https://mlsanity.com/paper/2607.23762/) (2026)

## Abstract (arXiv)

Generative recommendation has emerged as a transformative paradigm for capturing the dynamic evolution of user intents in sequential recommendation. While flow-based methods improve the efficiency of diffusion models, they remain hindered by the ``Noise-to-Data'' paradigm, which introduces two critical inefficiencies: prior mismatch, where generation starts from uninformative noise, forcing a lengthy recovery trajectory; and linear redundancy, where iterative solvers waste computation on modeling deterministic preference transitions. To address these limitations, we propose a Flow-based Average Velocity Establishment (Fave) framework for one-step generation recommendation that learns a direct trajectory from an informative prior to the target distribution. Fave is structured via a progressive two-stage training strategy. In Stage 1, we establish a stable preference space through dual-end semantic alignment, applying constraints at both the source (user history) and target (next item) to prevent representation collapse. In Stage 2, we directly resolve the efficiency bottlenecks by introducing a semantic anchor prior, which initializes the flow with a masked embedding from the user's interaction history, providing an informative starting point. Then we learn a global average velocity, consolidating the multi-step trajectory into a single displacement vector, and enforce trajectory straightness via a JVP-based consistency constraint to ensure one-step generation. Extensive experiments on three benchmarks demonstrate that Fave not only achieves state-of-the-art recommendation performance but also delivers an order-of-magnitude improvement in inference efficiency, making it practical for latency-sensitive scenarios.