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Bridging User Dynamics: Transforming Sequential Recommendations with Schrödinger Bridge and Diffusion Models

Wenjia Xie, Rui Zhou, Hao Wang, Tingjia Shen, Enhong Chen

TL;DR

This work tackles the challenge of personalization in sequential recommendation when diffusion-based methods are constrained by Gaussian priors that limit per-user information. By introducing the Schrödinger Bridge, the authors replace the Gaussian prior with the user’s current state $x_1$ and connect it to the target item embedding $x_0$, enabling direct modeling of the user-to-item transition. The proposed SdifRec architecture, with a connectivity model $f_\theta$, trains to reconstruct $x_0$ from intermediate SB states using a cross-entropy objective, and infers by iteratively sampling toward $x_0$ for ranking. An extended variant, con-SdifRec, leverages clustering-guided conditioning from LightGCN to incorporate collaborative information through a controllable guidance mechanism $w$, yielding further improvements. Experiments on three benchmark SR datasets show that SdifRec and con-SdifRec outperform strong baselines, with notable gains in efficiency (fewer sampling steps) and robustness across sequence lengths and item popularity, suggesting a practical path to personalized diffusion-based SR with flexible priors and multimodal guidance.

Abstract

Sequential recommendation has attracted increasing attention due to its ability to accurately capture the dynamic changes in user interests. We have noticed that generative models, especially diffusion models, which have achieved significant results in fields like image and audio, hold considerable promise in the field of sequential recommendation. However, existing sequential recommendation methods based on diffusion models are constrained by a prior distribution limited to Gaussian distribution, hindering the possibility of introducing user-specific information for each recommendation and leading to information loss. To address these issues, we introduce the Schrödinger Bridge into diffusion-based sequential recommendation models, creating the SdifRec model. This allows us to replace the Gaussian prior of the diffusion model with the user's current state, directly modeling the process from a user's current state to the target recommendation. Additionally, to better utilize collaborative information in recommendations, we propose an extended version of SdifRec called con-SdifRec, which utilizes user clustering information as a guiding condition to further enhance the posterior distribution. Finally, extensive experiments on multiple public benchmark datasets have demonstrated the effectiveness of SdifRec and con-SdifRec through comparison with several state-of-the-art methods. Further in-depth analysis has validated their efficiency and robustness.

Bridging User Dynamics: Transforming Sequential Recommendations with Schrödinger Bridge and Diffusion Models

TL;DR

This work tackles the challenge of personalization in sequential recommendation when diffusion-based methods are constrained by Gaussian priors that limit per-user information. By introducing the Schrödinger Bridge, the authors replace the Gaussian prior with the user’s current state and connect it to the target item embedding , enabling direct modeling of the user-to-item transition. The proposed SdifRec architecture, with a connectivity model , trains to reconstruct from intermediate SB states using a cross-entropy objective, and infers by iteratively sampling toward for ranking. An extended variant, con-SdifRec, leverages clustering-guided conditioning from LightGCN to incorporate collaborative information through a controllable guidance mechanism , yielding further improvements. Experiments on three benchmark SR datasets show that SdifRec and con-SdifRec outperform strong baselines, with notable gains in efficiency (fewer sampling steps) and robustness across sequence lengths and item popularity, suggesting a practical path to personalized diffusion-based SR with flexible priors and multimodal guidance.

Abstract

Sequential recommendation has attracted increasing attention due to its ability to accurately capture the dynamic changes in user interests. We have noticed that generative models, especially diffusion models, which have achieved significant results in fields like image and audio, hold considerable promise in the field of sequential recommendation. However, existing sequential recommendation methods based on diffusion models are constrained by a prior distribution limited to Gaussian distribution, hindering the possibility of introducing user-specific information for each recommendation and leading to information loss. To address these issues, we introduce the Schrödinger Bridge into diffusion-based sequential recommendation models, creating the SdifRec model. This allows us to replace the Gaussian prior of the diffusion model with the user's current state, directly modeling the process from a user's current state to the target recommendation. Additionally, to better utilize collaborative information in recommendations, we propose an extended version of SdifRec called con-SdifRec, which utilizes user clustering information as a guiding condition to further enhance the posterior distribution. Finally, extensive experiments on multiple public benchmark datasets have demonstrated the effectiveness of SdifRec and con-SdifRec through comparison with several state-of-the-art methods. Further in-depth analysis has validated their efficiency and robustness.
Paper Structure (30 sections, 1 theorem, 21 equations, 5 figures, 4 tables)

This paper contains 30 sections, 1 theorem, 21 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Sequential Recommendation
  4. Diffusion Models
  5. Schrödinger Bridge
  6. Preliminary
  7. Score-Based Generative Model
  8. Schrödinger Bridge Problem
  9. Problem Definition
  10. Methodology of SdifRec
  11. Build the Schrödinger Bridge
  12. Model Training
  13. Model Inferencing
  14. Method of Condition-guiding
  15. Introducing Conditional Information
  16. ...and 15 more sections

Key Result

Lemma 1

The result of Equation (eq7) can be obtained by: where $t \in[0,1]$, that is, let $T = 1$, and the values of $a$, $b$, etc. can be obtained from the following equation: and When $\epsilon \rightarrow 0$, $\widehat{\Psi}_{t}^{\epsilon}$, $\Psi_{t}^{\epsilon}$ converge to: $\widehat{\Psi}_{t}=\mathcal{N}\left(\alpha_{t} {x}_{0}, \alpha_{t}^{2} \sigma_{t}^{2} \boldsymbol{I}\right)$, $\quad \Psi_{t

Figures (5)

  • Figure 1: An example illustrates the difference between our motivation and existing diffusion-based methods.
  • Figure 2: Framework of SdifRec. The bottom left part of the figure illustrates the method of con-SdifRec.
  • Figure 3: The influence of different numbers of clustering centers and guidance strength on the results of con-SdifRec.
  • Figure 4: The impact of sample steps on SdifRec and DiffuRec.
  • Figure 5: Performance comparison between SdifRec, DiffuRec and SASRec under different items and sequence lengths on the Amazon Beauty dataset.

Theorems & Definitions (1)

  • Lemma 1