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OT-FlowRec: Optimal Transport-Guided Multi-Bridge Flow for Multimodal Sequential Recommendation
Miao Sun
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Abstract
Abstract:E-commerce user preferences evolve dynamically within sessions, exhibiting concurrent and multi-centric interest distributions. While existing multimodal sequential recommendation methods leverage global attention to compress historical interactions, they inadequately capture the concurrent nature of multi-interest behaviors and fail to model the underlying multi-centric distribution of user intent. To tackle this issue, we propose OT-FlowRec, an optimal transport-guided multi-bridge flow matching framework that explicitly models multi-interest distributions to facilitate multimodal sequential recommendation. Unlike single-path generative models, OT-FlowRec constructs a mixture of parallel, interest-specific transport flows to model the multi-centric distribution characteristics, where each flow preserves a distinct user interest cluster via an optimal transport plan. Then, a geometric transport mechanism is designed to establish minimum-cost paths from the latent multi-interest distribution to target preference prototypes to provide multi-interest awareness. Moreover, a progressive time-sampling warmup strategy dynamically biases optimization weights toward the final states of the generation process, bridging the gap between continuous global distribution fitting and practical top-$k$ ranking metrics. This approach achieves explicit interest disentanglement, ensuring the preservation of a multi-peaked preference representation instead of collapsing it into a unimodal average. Extensive experiments on three public datasets demonstrate that OT-FlowRec outperforms existing state-of-the-art baselines.
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- Source: https://arxiv.org/abs/2610.16038v1
- Canonical: https://arxiv.org/abs/2610.16038v1
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OT-FlowRec: Optimal Transport-Guided Multi-Bridge Flow for Multimodal Sequential Recommendation Miao Sun Affiliation: Nanjing University of Science and Technology School of Computer Science and Engineering Email: miao.sun@njust.edu.cn Abstract E-commerce user preferences evolve dynamically within sessions, exhibiting concurrent and multi-centric interest distributions. While existing multimodal sequential recommendation methods leverage global attention to compress historical interactions, they inadequately capture the concurrent nature of multi-interest behaviors and fail to model the underlying multi-centric distribution of user intent. To tackle this issue, we propose OT-FlowRec, an optimal transport-guided multi-bridge flow matching framework that explicitly models multi-interest distributions to facilitate multimodal sequential recommendation. Unlike single-path generative models, OT-FlowRec constructs a mixture of parallel, interest-specific transport flows to model the multi-centric distribution characteristics, where each flow preserves a distinct user interest cluster via an optimal transport plan. Then, a geometric transport mechanism is designed to establish minimum-cost paths from the latent multi-interest distribution to target preference prototypes to provide multi-interest awareness. Moreover, a progressive time-sampling warmup strategy dynamically biases optimization weights toward the final states of the generation process, bridging the gap between continuous global distribution fitting and practical top-k ranking metrics. This approach achieves explicit interest disentanglement, ensuring the preservation of a multi-peaked preference representation instead of collapsing it into a unimodal average. Extensive experiments on three public datasets demonstrate that OT-FlowRec outperforms existing state-of-the-art baselines. 1 Introduction Multimodal sequential recommendation (MSR) has emerged as a pivotal paradigm for delivering personalized services in e-commerce, driven by its capacity to model the temporal dynamics of user preferences. By synergistically integrating interaction sequences with complementary signals derived from text and images, MSR is advantageous in disambiguating items that share similar behavioral footprints yet differ semantically, meanwhile enriching preference inference from sparse or inherently noisy user interactions. This enables MSR to capture users’ nuanced, often concurrent interests—a capability that pure sequential models lack, and has drawn growing research attention. (Pan et al., 2026; Hu et al., 2023; Liu et al., 2024a; Ji et al., 2023; Liu et al., 2024c; Xu et al., 2025; Xv et al., 2024; Wei et al., 2023; Zhang et al., 2024a; Liu et al., 2024b; Fang et al., 2024). A substantial body of research has been devoted to MSR, which can be categorized into three technical lines: traditional sequential methods, diffusion-based methods, and flow-based methods. Specifically, traditional sequential methods use recurrent networks or self-attention to capture ordered dependencies through discriminative learning (Hidasi et al., 2016; Kang and McAuley, 2018; Sun et al., 2019). Diffusion-based methods learn stochastic denoising processes in continuous spaces, improving robustness to noisy interactions and supporting flexible generation of target-item representations (Xie et al., 2024; Li et al., 2023; Yang et al., 2023; Liu et al., 2025c). Flow-based methods employ vector-field learning and deterministic ODE evolution, reducing the stochasticity and iterative cost of diffusion sampling while directly modeling continuous preference trajectories (Liu et al., 2025b; Liu et al., 2025a; Huang et al., 2025; Li et al., 2025b). Figure 1: User interaction paths in the Toys dataset. Colors denote latent interest categories; this shows that multiple interests coexist within a session. Although promising success has been achieved by previous works, two primary limitations remain. (i) Multi-centric interest distribution collapse. Existing global attention-based approaches compress multi-peaked interactions into single deterministic embeddings, which fail to describe the intrinsic multi-centric distribution characteristics. Moreover, most existing diffusion-based and flow-based methods construct single-peaked distribution representation, which is insufficient to model the multi-centric distribution of user intent. (Kang and McAuley, 2018; Sun et al., 2019; Yang et al., 2023; Hu et al., 2024; Liu et al., 2025b; Li et al., 2025b) (Figure 1). (i) Static transport with misaligned priors. Prevailing flow-based generative recommenders construct time-dependent conditional paths based on independently sampled prior distributions, without accounting for the underlying optimal transport geometry between users’ historical interactions and their target preferences. Consequently, the learned trajectories are directionally unconstrained and lack semantic grounding to the multi-interest prototypes (Lipman et al., 2023; Tong et al., 2024; Liu et al., 2025a). To address these limitations, we propose OT-FlowRec, an optimal transport-guided multi-bridge flow matching framework. Rather than collapsing a complex interaction sequence into a single representation, a Multi-Prototype Guided Source Distribution (MPSD) module is constructed to represent concurrent user preferences with multi-interest source distribution. Its interest-specific components initialize parallel transport flows, preserving the underlying multi-peaked structure and avoiding unimodal collapse. Considering the advantage of interest prototypes (Wang et al., 2023a) in capturing diverse user semantics, an OT-Guided Multi-Bridge Flow Matching (OT-MBFM) module is further built, where multiple preference prototypes are first constructed. Accordingly, an interest distribution-to-prototype transformation learning process is then designed to map the multiple interest distribution to their matched prototypes through those parallel transport flows. To facilitate the transformation, minimum-cost paths are computed to connect the latent source distribution to target preference prototypes, ensuring explicit awareness of diverse user interests during generation. Furthermore, a mismatch remains between continuous distribution fitting and discrete ranking evaluation during the sampling process. We therefore develop a Progressive Time-sampling Warmup (PTW) that progressively shifts optimization toward the terminal states of the generation trajectory. By focusing training on these later states, PTW narrows the gap between continuous trajectory fitting and top-k ranking. The main contributions are summarized as follows: • We propose OT-FlowRec, a multi-bridge flow learning framework that explicitly encodes the intrinsic multi-centric distribution of user interests. Unlike global attention mechanisms that compress concurrent interests into single deterministic embeddings, OT-FlowRec constructs a mixture of parallel, interest-specific transport flows, achieving effective multi-interest disentanglement while avoiding the multi-centric interest distribution collapse commonly observed in global attention methods. • We propose the OT-MBFM module which establishes minimum-cost paths from the latent multi-interest distribution to target preference prototypes, providing directionally constrained trajectories. Specifically, a PTW strategy is designed to improve ranking quality by dynamically shifting optimization weights towards the terminal generative states, which effectively aligns continuous distribution fitting with top-k ranking metrics. • Extensive experiments on three public datasets demonstrate that our framework outperforms existing state-of-the-art baselines across all evaluation metrics. 2 Methodology 2.1 Preliminaries In sequential multimodal recommendation, the user set is defined as U=u1,u2,…,u|U|U=\u_1,u_2,…,u_|U|\ and the item set is defined as I=i1,i2,…,i|I|I=\i_1,i_2,…,i_|I|\. For each user u∈Uu∈ U, the sequence of historically interacted items is represented by Su=[i1(u),i2(u),…,in(u)]S_u=[i_1^(u),i_2^(u),…,i_n^(u)], where n denotes sequence length. 2.2 Overall Framework Figure 2 shows OT-FlowRec coordinating three modules to transform multimodal interaction sequences into top-k recommendation lists. Given multimodal interaction sequences, OT-FlowRec fuses item ID embeddings with pre-trained visual and textual features via a softplus gating network. Matching these representations against a learnable prototype space selects top-k responsive prototypes to initialize parallel interest-specific bridges. An optimal transport (OT) matrix couples these bridges with target preference prototypes along minimum-cost trajectories, letting a vθv_θ-guided ODE solver integrate states over t∈[0,1]t∈[0,1] into k terminal representations. During training, a dynamic Beta distribution replaces uniform sampling, shifting weights toward late intervals to align trajectory fitting with discrete ranking objectives. At inference, a bridge score aggregation layer max-pools inner products between terminal states and candidate item embeddings for top-k recommendations. Figure 2: The overall architecture of OT-FlowRec. Top: The end-to-end recommendation pipeline, transforming multimodal item interactions into parallel transport flows. Middle-left: MPSD fuses multimodal features via a softplus gating network and extracts top-k prototypes to construct parallel interest distributions. Bottom-right: OT-MBFM establishes OT couplings via a geometric cost matrix to guide deterministic flow matching along minimum-cost trajectories. Bottom-left: PTW dynamically shifts time-step sampling weights toward terminal generation states (t→1t→ 1) via Beta distribution adjustments. 2.3 Multi-Prototype Guided Source Distribution We propose the MPSD module to explicitly disentangle concurrent user preferences. Rather than compressing multimodal interactions into a single representation via global attention (Kang and McAuley, 2018; Sun et al., 2019; Lin et al., 2024), MPSD evaluates user responsiveness to multi-interest prototypes. By selecting top-k prototypes to construct independent ODE paths, it forms parallel transport flows that preserve multi-peaked distribution of next-item preferences. To exploit the multimodal semantics of items, a softplus gating network is designed to dynamically fuse collaborative filtering signals and modal features. For any item i in the sequence and modality m∈id,v,tm∈\id,v,t\, its multimodal fused representation xi∈ℝdx_i ^d is calculated as follows: gm=Softplus(Wm[eid‖ev‖et]+bm),g_m=Softplus (W_m [e_id\|e_v\|e_t ]+b_m ), (1) xi=gid⊙eid+gv⊙ev+gt⊙et,x_i=g_id e_id+g_v e_v+g_t e_t, (2) where Wm∈ℝd×3dW_m ^d× 3d and bm∈ℝdb_m ^d are learnable mapping parameters. This gating mechanism adaptively weights different modalities to accurately capture item characteristics. To disentangle multiple user interests, a globally learnable interest prototype space P=[p1,p2,…,pM]∈ℝM×dP=[p_1,p_2,…,p_M] ^M× d is constructed, where M is the total number of prototypes. The model extracts the most recent fine-grained preference state hu∈ℝdh_u ^d, which combines the last hidden state with the sequence representation and calculates its normalized response score sjs_j with respect to all candidate prototypes pjp_j as follows: sj=exp(hu⊤pj/τ)∑m=1Mexp(hu⊤pm/τ),s_j= (h_u p_j/τ) _m=1^M\, (h_u p_m/τ), (3) where τ is the temperature parameter. This score quantifies the alignment between the user state and latent interests for subsequent prototype selection. We extract the top-k prototypes with the highest response scores instead of a global weighted average to preserve the multi-peaked nature of diverse user interests. The index set of the selected prototypes KpK_p is defined as follows: Kp=TopK(s1,…,sM).K_p=TopK (s_1,…,s_M ). (4) Consequently, the representation strategy is transformed into a mixture of parallel, interest-specific transport flows. This design achieves interest disentanglement, thereby maintaining a robust multi-peaked preference representation. 2.4 OT-Guided Multi-Bridge Flow Matching This section details the OT-MBFM module, which constructs deterministic transport trajectories from the latent multi-interest distribution to target preference prototypes. It minimizes geometric transport cost to derive an optimal coupling that guides continuous representation generation. Assume that the selected top-k interest prototype matrix Ptgt∈ℝ|Kp|×dP_tgt ^|K_p|× d serves as the support set for the target distribution. The geometric transport cost matrix C∈ℝn×|Kp|C ^n×|K_p| between the latent multi-interest distribution PsrcP_src and PtgtP_tgt is formulated as Cj,k=‖xj−pk‖22C_j,k=\|x_j-p_k\|_2^2. The marginal masses are specified in Appendix A. By introducing Sinkhorn entropy regularization (Cuturi, 2013), the OT plan π⋆∈ℝn×|Kp|π ^n×|K_p| is obtained as follows: π⋆=argmin∑j,kπ∈Π(Psrc,Ptgt)πj,kCj,k−ϵH(π),π = _π∈ (P_src,P_tgt)\, _j,k\, _j,kC_j,k-ε H(π), (5) H(π)=−∑j,kπj,klogπj,k,H(π)=- _j,k\, _j,k _j,k, (6) where Π(⋅,⋅) (·,·) is the set of all joint probability measures that satisfy the marginal distribution constraints, and ϵε denotes a hyperparameter controlling smoothness. Based on π⋆π , the framework softly assigns historical sequence items to corresponding target preference prototypes, thereby forming multiple parallel flow matching bridges. For any time-step t∈[0,1]t∈[0,1], a deep neural network vθ(x,t)v_θ(x,t) parameterizes the target vector field vt(x)v_t(x). Guided by the OT plan, the conditional vector field transitions from random pairing to deterministic matching along optimal geometric paths. By establishing minimum-cost transport paths, the OT-MBFM module equips the framework with explicit multi-interest awareness throughout continuous generation. 2.5 Progressive Time-sampling Warmup This section details the PTW strategy, designed to align continuous generative objectives with discrete top-k ranking metrics. By dynamically shifting optimization weights toward the terminal states of the generation trajectory, the PTW strategy ensures that the vector field precision is concentrated where practical recommendation ordering is determined. Specifically, the strategy employs the Beta distribution to replace the standard uniform distribution U(0,1)U(0,1) for sampling the integration time-step t. The shape parameter α is dynamically adjusted as training progresses: t∼Beta(α,1).t (α,1 ). (7) This formulation establishes a time-dependent weighting mechanism to prioritize late-stage generation. During the early stages of training, setting α≈1α≈ 1 reduces the process to uniform sampling, which prompts the model to capture the global vector field. As training advances, α is gradually increased to bias the sampling probability toward the high time-step interval approaching 11. Consequently, this mechanism transitions the optimization focus from global distribution modeling to terminal state refinement, bridging continuous distribution fitting and discrete ranking evaluation. 2.6 Optimization This section details the end-to-end optimization of OT-FlowRec. To guide continuous representation generation and discrete item ranking, the framework minimizes a combined loss function LtotalL_total: ℒtotal=λ1ℒFM+λ2ℒCE+λ3ℒOT+λ4ℒProto,L_total= _1L_FM+ _2L_CE+ _3L_OT+ _4L_Proto, (8) where ℒFML_FM, ℒCEL_CE, ℒOTL_OT, and ℒProtoL_Proto denote the flow matching loss, the cross-entropy ranking loss, the OT geometric regularization, and the prototype orthogonality constraint, respectively, with λ⋅ _· representing weighting hyperparameters tuned via Bayesian optimization. To drive representation generation along the deterministic geometric paths established by the OT-MBFM module, the target vector field vt(x)v_t(x) at time-step t∈[0,1]t∈[0,1] is parameterized by a deep neural network vθ(x,t)v_θ(x,t). The flow matching loss ℒFML_FM is defined as follows: ℒFM(θ)=t∼Beta(α,1),(x0,x1)∼π⋆[‖vθ(xt,t)−(x1−x0)‖22],L_FM(θ)=E_ subarrayct (α,1),\\ (x_0,x_1) π subarray [ \|v_θ(x_t,t)-(x_1-x_0) \|_2^2 ], (9) where xt=(1−t)x0+tx1x_t=(1-t)x_0+tx_1 represents interpolated state along OT path. This loss guides continuous representation generation along minimum-cost transport paths. Bridging continuous generation and discrete ranking, ℒCEL_CE injects a collaborative filtering signal by aggregating the terminal states x1(k)x_1^(k) over the selected prototypes KpK_p. Specifically, we define the bridge score for item j as sj=maxk∈Kp⟨x1(k),ej⟩/τces_j= _k∈ K_p x_1^(k),e_j / _ce and maximize the likelihood of the ground-truth next item in+1i_n+1: ℒCE=−∑u∈logexp(sin+1)∑j∈ℐexp(sj),L_CE=- _u (s_i_n+1 ) _j (s_j ), (10) where τce _ce is the temperature and e denotes item embeddings. To prevent unconstrained generation in semantic spaces, we regularize vector field using the Sinkhorn optimal coupling π⋆π between source distribution and target prototypes for each bridge: ℒOT=∑j=1n∑k∈Kpπj,k⋆‖xj−pk‖22−ϵH(π⋆),L_OT= _j=1^n _k∈ K_p _j,k x_j-p_k _2^2-ε H (π ), (11) with entropy regularizer H(⋅)H(·). This regularization guides generation trajectories along minimal-effort transport paths. Finally, the orthogonality constraint ℒProtoL_Proto on the row-normalized matrix P~ P maintains semantic capacity against mode collapse: ℒProto=‖P~P~⊤−IM‖F2.L_Proto=\| P P -I_M\|_F^2. (12) This constraint disperses prototypes uniformly to capture multi-peaked interest independently. We optimize the framework using Adam. During inference, the selected branches share the initial state x0(k)=hux_0^(k)=h_u, the Euler ODE solver integrates along the learned vector field: x1(k)=x0(k)+∫01vθ(xt(k),t∣pk)t,∀k∈Kp,x_1^(k)=x_0^(k)+ _0^1v_θ(x_t^(k),t p_k)\,dt, ∀ k∈ K_p, (13) where the resulting terminal states x1(k)x_1^(k) serve as the predicted multi-interest representation. Finally, these representations are matched against candidate item embeddings via max-pooling aggregation to generate the top-k recommendations. 3 Experiments 3.1 Experiment Setting To evaluate the effectiveness of the proposed OT-FlowRec in sequential multimodal recommendation tasks, we design and conduct comprehensive experiments. Specifically, the experiments are guided by three primary research questions: RQ1: We investigate whether OT-FlowRec consistently outperforms existing sequential, multimodal, and generative recommendation baselines across real-world datasets characterized by varying sequence lengths and item domains. RQ2: We explore how the key modules of OT-FlowRec, including MPSD, OT-MBFM, and PTW, contribute to the overall recommendation performance, and we analyze the specific roles they play within the model. RQ3: We examine how the proposed MPSD, OT-MBFM, and PTW modules improve recommendation performance and generation quality compared with traditional generative recommendation models that rely on single global representations and standard flow matching. 3.1.1 Datasets and Evaluation Metrics Table 1: Statistics of the evaluation datasets. Dataset Users Items Inter. Sparsity Avg. Len. Beauty 22364 12102 198502 99.92% 8.8 Video Games 24304 10679 231780 99.91% 9.5 Toys 19413 11925 167597 99.92% 8.6 We conduct experiments on three widely used Amazon datasets (McAuley et al., 2015): Beauty, Video Games, and Toys (statistics in Table 1). These datasets cover distinct item domains, representing cosmetics and personal care, gaming consoles and accessories, and children’s entertainment products. For a fair comparison, we adopt Hit Rate (H@K) and Normalized Discounted Cumulative Gain (N@K) with K∈10,20K∈\10,20\ to assess top-k recall and ranking quality, respectively. 3.1.2 Baseline Methods To evaluate OT-FlowRec, we compare it against three categories of baseline methods: (1) Traditional sequential models, including RNN-based and Transformer-based architectures (GRU4Rec (Hidasi et al., 2016), SASRec (Kang and McAuley, 2018), BERT4Rec (Sun et al., 2019)) and those integrating side information (MSSR (Lin et al., 2024)); (2) Diffusion-based models, spanning foundational frameworks (DreamRec (Yang et al., 2023), DiffuRec (Li et al., 2023)) and advanced variants (DiffMM (Jiang et al., 2024), ADRec (Chen et al., 2025), MoDiCF (Li et al., 2025a), PreferDiff (Liu et al., 2025c)); and (3) Flow-based models tailored for recommendation (FMRec (Liu et al., 2025b), FlowCF (Liu et al., 2025a), FindRec (Wang et al., 2025)). 3.1.3 Implementation Details We implement the proposed method using the widely adopted RecBole (Zhao et al., 2021) framework. For all datasets, we filter out users and items with fewer than 5 interactions and truncate historical sequences to a maximum length of 50. The models are trained for up to 300 epochs using the Adam optimizer, with a training batch size of 1024 and an evaluation batch size of 4096. We apply an early-stopping strategy if validation performance does not improve for 5 consecutive evaluations. Performance is evaluated using Hit and NDCG at K∈10,20K∈\10,20\. Textual and visual features are extracted using BERT (Devlin et al., 2019) (768 dimensions) and CLIP-ViT (Radford et al., 2021) (512 dimensions), respectively, which are then mapped to the hidden dimension d via linear layers. All experiments are conducted on a single NVIDIA RTX A6000 GPU. For further experimental details, see Appendix D. 3.2 RQ1: Overall Performance Table 3 demonstrates that OT-FlowRec outperforms all three baseline categories across all datasets and top-k metrics, achieving average performance improvements of 25.08% in H@20 and 9.15% in N@20 across the three datasets. Comparison with traditional sequential models. Traditional sequential baselines compress complex historical interactions into a single deterministic representation via global attention, inducing unimodal collapse that prevents capturing concurrent multi-interest behaviors. Through the MPSD module, OT-FlowRec explicitly disentangles interactions into parallel, interest-specific transport flows to preserve multi-peaked interest distributions. Consequently, compared with MSSR, which is the strongest baseline in this category, OT-FlowRec achieves substantial improvements on Beauty dataset, increasing H@20 by 32.53% and N@20 by 19.86%. Comparison with diffusion-based models. Continuous diffusion models suffer from unguided and curved diffusion paths. In contrast, OT-FlowRec replaces stochastic denoising with deterministic flow matching along OT paths. By establishing explicit minimum-cost connections between source distributions and target prototypes via the OT-MBFM module, the framework significantly stabilizes generation. Compared with ADRec, the top-performing diffusion baseline, OT-FlowRec demonstrates notable gains on Video Games, improving H@20 by 27.69% and N@20 by 10.63%. Comparison with flow-based models. Existing flow-based recommendation baselines ignore semantic transport distances by relying on randomly paired Euclidean straight paths and uniform time sampling, which misaligns continuous trajectory fitting with discrete ranking objectives. OT-FlowRec resolves these bottlenecks through OT couplings and the PTW strategy. Biasing optimization weights toward terminal generation states (t→1t→ 1) concentrates vector field precision where discrete item ranking occurs. Compared with FlowCF, the strongest flow-based competitor, OT-FlowRec drives NDCG improvements, increasing N@20 by 9.81% over FlowCF on Beauty. Table 2: Overall performance. The best and second-best scores are shown in bold and underlined, respectively. Baseline Beauty Video Games Toys H@10 H@20 N@10 N@20 H@10 H@20 N@10 N@20 H@10 H@20 N@10 N@20 SASRec 0.0401 0.0660 0.0200 0.0265 0.0847 0.1281 0.0423 0.0532 0.0322 0.0497 0.0164 0.0208 GRU4Rec 0.0562 0.0851 0.0298 0.0370 0.0725 0.1122 0.0376 0.0475 0.0454 0.0676 0.0260 0.0316 BERT4Rec 0.0379 0.0571 0.0200 0.0249 0.0708 0.1091 0.0361 0.0456 0.0274 0.0395 0.0154 0.0184 MSSR 0.0583 0.0956 0.0314 0.0448 0.0709 0.1283 0.0415 0.0515 0.0613 0.0950 0.0318 0.0410 DreamRec 0.0228 0.0417 0.0130 0.0176 0.0415 0.0712 0.0221 0.0295 0.0216 0.0391 0.0111 0.0155 DiffuRec 0.0548 0.0939 0.0263 0.0354 0.0617 0.0795 0.0278 0.0433 0.0725 0.0982 0.0366 0.0430 DiffMM 0.0556 0.0975 0.0225 0.0361 0.0651 0.1064 0.0333 0.0438 0.0416 0.0664 0.0214 0.0276 ADRec 0.0673 0.0945 0.0417 0.0485 0.1059 0.1538 0.0584 0.0705 0.0704 0.0909 0.0421 0.0512 MoDiCF 0.0531 0.0821 0.0263 0.0335 0.0585 0.0948 0.0292 0.0383 0.0496 0.0724 0.0254 0.0312 PreferDiff 0.0594 0.0675 0.0350 0.0471 0.0735 0.0838 0.0552 0.0578 0.0463 0.0489 0.0334 0.0341 FMRec 0.0531 0.1069 0.0358 0.0459 0.0918 0.1370 0.0477 0.0593 0.0838 0.1013 0.0426 0.0501 FlowCF 0.0502 0.1075 0.0349 0.0489 0.0744 0.1050 0.0427 0.0505 0.0650 0.0804 0.0360 0.0450 FindRec 0.0549 0.0770 0.0318 0.0374 0.0911 0.1394 0.0465 0.0586 0.0703 0.0959 0.0440 0.0505 ours 0.0891 0.1267 0.0442 0.0537 0.1276 0.1964 0.0607 0.0780 0.0946 0.1314 0.0455 0.0548 Improv. 32.39% 17.86% 5.99% 9.81% 20.49% 27.69% 3.93% 10.63% 12.88% 29.71% 3.40% 7.03% Table 3: Ablation study results. Variant Beauty Video Games Toys H@10 H@20 N@10 N@20 H@10 H@20 N@10 N@20 H@10 H@20 N@10 N@20 w/o MPSD 0.0866 0.1249 0.0431 0.0515 0.1241 0.1948 0.0590 0.0776 0.0934 0.1299 0.0437 0.0529 w/o OT-MBFM 0.0874 0.1253 0.0435 0.0531 0.1239 0.1936 0.0589 0.0764 0.0913 0.1303 0.0446 0.0544 w/o PTW 0.0863 0.1257 0.0428 0.0527 0.1244 0.1919 0.0587 0.0757 0.0942 0.1299 0.0438 0.0529 ours 0.0891 0.1267 0.0442 0.0537 0.1276 0.1964 0.0607 0.0780 0.0946 0.1314 0.0455 0.0548 3.3 RQ2: Ablation Study To assess the individual contributions of core designs in OT-FlowRec, we evaluate three ablation variants across the Beauty, Video Games, and Toys datasets (Table 3). At the representation level, constructing parallel, interest-specific transport flows is core to disentangling concurrent user behaviors and preserving multi-peaked interest distributions. Removing the multi-prototype mechanism (w/o MPSD) compresses complex historical interactions into a single global representation, degrading performance across all evaluation metrics. For instance, on the Beauty dataset, H@10 drops from 0.0891 to 0.0866. Moreover, establishing minimum-cost geometric paths from the latent multi-interest distribution to target preference prototypes contributes to explicit multi-interest awareness and mitigates trajectory conflicts. Replacing OT guidance with randomly paired Euclidean straight paths (w/o OT-MBFM) fails to capture complex behavioral sequences, causing performance declines. Specifically, H@10 decreases from 0.1276 to 0.1239 on the Video Games dataset. During the optimization phase, dynamically shifting training weights toward terminal generation states is beneficial for continuous distribution fitting with discrete top-k ranking metrics. Substituting the PTW strategy with uniform time-sampling (w/o PTW) ignores ranking sensitivity to late-stage integration precision (t→1t→ 1). Consequently, this variant impairs ranking accuracy across all datasets, as evidenced by N@20 dropping from 0.0780 to 0.0757 on the Video Games dataset. 3.4 RQ3: Qualitative Analysis Figure 3: Vector field comparison between traditional flow matching and OT-FlowRec on the Toys. Figure 3 shows the vector field directions of both traditional random-pairing flow matching and OT-FlowRec at different integration times. According to Figure 3, traditional flow matching produces conflicting directions and extensive region ambiguity, with directional consistency falling to 0.180.18 and the ambiguity rate rising to 90.0%90.0\% at t=0.5t=0.5. In contrast, OT-FlowRec maintains directional consistency above 0.950.95 and ambiguity below 1.1%1.1\% across all three time steps, resulting in more coherent transport trajectories. The comparison of vector field direction demonstrates that OT-guided coupling in OT-FlowRec provides directionally constrained trajectories. The t-SNE and transport-cost analyses are presented in Appendix C(Figures 5 and 5) and training stability is presented in Appendix E. 4 Related Work 4.1 Traditional Sequential Recommendation Traditional sequential recommendation methods primarily learn behavior transition patterns from user historical interaction sequences (Cen et al., 2020; Li et al., 2024; Zhang et al., 2024b; Chen et al., 2022; Qin et al., 2024; Wang et al., 2019; Li et al., 2019; Tan et al., 2021; Pan et al., 2026; Park et al., 2025; Duan et al., 2025; Hou et al., 2022). Early approaches utilized Markov chains, RNNs (Hidasi et al., 2016), and CNNs (Tang and Wang, 2018), which were later broadly superseded by Transformer-based architectures like SASRec (Kang and McAuley, 2018) and BERT4Rec (Sun et al., 2019) to better capture sequence dependencies. To alleviate interaction sparsity, subsequent research incorporated auxiliary multimodal information (e.g., text and images) (Hu et al., 2023; Wang et al., 2024; Liu et al., 2024a; Kim et al., 2025; Ji et al., 2023; Liu et al., 2024c; Xu et al., 2025; Yang et al., 2025; Zhang et al., 2025; Xv et al., 2024; Wei et al., 2023; Zhang et al., 2024a; Liu et al., 2024b; Fang et al., 2024), utilizing techniques like multi-sequence attention (Lin et al., 2024) and modality experts (Guo et al., 2025). However, these methods typically remain within the discriminative modeling paradigm, compressing complex user behaviors into deterministic, single-point representations. This limitation prevents them from fully capturing the multi-peaked distributional nature and generative evolution of dynamic user interests. 4.2 Diffusion-Based Recommendation Diffusion-based methods shift recommendation from discriminative matching to generative distribution modeling (Xie et al., 2024; Chen et al., 2025; Cui et al., 2025; Jiang et al., 2024; Liu et al., 2023; Li et al., 2025a; Qu and Nobuhara, 2025; Mao et al., 2025; Liu et al., 2025c; Wang et al., 2023b). Early works like DiffuRec (Li et al., 2023) and DreamRec (Yang et al., 2023) reconstruct target item representations via stochastic noise-addition and reverse denoising processes, thereby capturing diverse user interests as continuous distributions rather than fixed vectors. Subsequent research has enhanced this paradigm by integrating multimodal user-item graphs (Jiang et al., 2024), aligning generation with personalized ranking objectives (Liu et al., 2025c), and employing token-level diffusion to prevent embedding collapse (Chen et al., 2025). Despite these advancements, the inherent reliance on curved probability paths and multi-step stochastic sampling limits their inference efficiency and often leads to error accumulation during the generative process. 4.3 Flow-Based Recommendation Flow-based models replace the stochastic denoising of diffusion models with deterministic continuous generation, transporting prior distributions to target distributions via time-dependent vector fields (Lipman et al., 2023; Tong et al., 2024). Recent works have adapted flow matching for recommendation by designing discrete flows for implicit feedback (Liu et al., 2025a), utilizing straight trajectories to reduce preference perturbations (Liu et al., 2025b), and employing Stein-guided entropic flows to capture multi-peaked sequential preferences (Wang et al., 2025). Despite improving inference efficiency and stability over diffusion models, existing flow matching methods typically construct simple, global straight paths. This ignores the explicit geometric transport costs between historical distributions and latent multi-interest prototypes. Furthermore, their continuous distribution fitting objectives often misalign with discrete top-k ranking metrics. To bridge these gaps, our OT-FlowRec proposes OT-MBFM for explicit interest disentanglement, alongside the PTW strategy to directly optimize late-stage generation for practical ranking accuracy. 5 Conclusion In this paper, we proposed OT-FlowRec to jointly model concurrent user interests in multimodal sequential recommendation. To overcome unimodal collapse, our framework constructed parallel transport flows that disentangled diverse interests and preserved multi-peaked preference distributions. Integrating minimum-cost geometric transport paths with the progressive time-sampling warmup strategy achieved explicit multi-interest awareness and bridged continuous distribution fitting and discrete top-k ranking metrics. Extensive experiments across three datasets demonstrated that OT-FlowRec outperformed state-of-the-art baselines. AI use statement AI tools were used to polish the writing of this paper. References Cen et al. (2020) Y. Cen, J. Zhang, X. Zou, C. Zhou, H. Yang, and J. 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Appendix A Marginal Distributions for Optimal Transport For a user with n valid Transformer states, let ℓ=min(n,L) = (n,L), where L is the maximum source-window length. The source and target distributions are Psrc=∑j=1ℓajδxn−ℓ+j,Ptgt=∑k=1Mskδpk,aj=exp[−γ(ℓ−j)]∑q=1ℓexp[−γ(ℓ−q)],P_src= _j=1 a_j _x_n- +j, P_tgt= _k=1^Ms_k _p_k, a_j= [-γ( -j)] _q=1 [-γ( -q)], (14) where δ denotes a point mass, γ controls recency weighting, and sks_k is the normalized prototype response defined in the main text. Padding positions are excluded. The feasible couplings satisfy Π(Psrc,Ptgt)=π∈ℝ+ℓ×M:π|Kp|=,π⊤ℓ=. (P_src,P_tgt)=\π _+ × M: 1_|K_p|=a,\ π 1_ =s\. (15) Appendix B Problem Formulation Given the multimodal context, each item i∈Ii∈ I comprises an ID embedding eid∈ℝde_id ^d, a visual feature ev∈ℝde_v ^d and a textual feature et∈ℝde_t ^d, where d represents the dimension of the latent feature space. Formally, given the historical interaction sequence SuS_u, the core task is to learn a continuous generative mapping function fθ(⋅)f_θ(·) to predict the item in+1(u)∈Ii_n+1^(u)∈ I with the most likely to interact in the next time-step n+1n+1. Appendix C Qualitative Analysis (RQ3) Figure 5 shows the comparison between t-SNE projections (van der Maaten and Hinton, 2008) of historical item embeddings and the global mean-pooled state with the interest anchors learned by OT-FlowRec. A mean-pooled state represents these clusters with a single central point, whereas the learned anchors align with different clusters and retain the multi-peaked structure of concurrent user interests. This advantage arises from the MPSD model, which preserves interest-specific representations instead of averaging the entire interaction history into a single vector. Figure 4: T-SNE visualization of user multi-interest behaviors on the Toys dataset. (a) A single averaged state suppresses minority interests; (b) multi-interest anchors preserve the semantic structure. Figure 5: A comparison of transport costs between traditional flow matching and OT-FlowRec. Beyond preserving the multi-peaked interest structure, Figure 5 compares transport costs of OT-FlowRec with traditional flow matching based on random pairings. OT-FlowRec lowers the average transport cost by 24.2% on three datasets, indicating better efficiency from source distribution to target preference prototypes. The improvement of OT-guided may be attributed to the coupling mechanism defined in Equation (11), which jointly minimizes the trajectory costs of multiple bridges. Appendix D Additional Implementation Details We further tune OT-FlowRec on each dataset using validation Hit@10. Unless otherwise specified, we fix the number of attention heads to 2, the feed-forward dimension to 512, the time-embedding dimension to 32. The pre-extracted visual and textual features are kept frozen and are projected into the hidden space by two-layer MLPs. The final item representation is obtained by a trainable softplus-gated fusion of ID, visual, and textual embeddings. The user state is computed as the average of the last Transformer state and the mean-pooled valid sequence states. The entropic OT coupling is solved by Sinkhorn iterations with regularization ϵOT _OT, and the OT loss uses the expected squared transport cost under this coupling. For multi-prototype bridge inference, the top-k prototypes are used as bridge conditions and their scores are aggregated by max pooling. We optimize softmax cross-entropy over all items. The hyperparameter search space is summarized in Table 4. Log-uniform parameters are sampled as exp([a,b]) (U[a,b]). The dataset-specific best configurations selected on the validation set are reported in Table 5. After hyperparameter selection, each final configuration is rerun with five random seeds 2022,2023,2024,2025,2026\2022,2023,2024,2025,2026\, and we report the mean performance over these runs. Table 4: Hyperparameter search space of OT-FlowRec. Hyperparameter Search space Learning rate exp([−9.2,−6.0]) (U[-9.2,-6.0]) Number of Transformer layers 1,2,3\1,2,3\ Hidden dimension d 128,256\128,256\ Hidden dropout / attention dropout [0.1,0.5]U[0.1,0.5] Number of prototypes M 32,64,96,128\32,64,96,128\ ODE steps 2,4,6,8\2,4,6,8\ Prototype temperature τproto _proto exp([−4.2,−1.9]) (U[-4.2,-1.9]) Sinkhorn regularization ϵOT _OT exp([−4.0,−1.6]) (U[-4.0,-1.6]) Sinkhorn iterations 5,10,20\5,10,20\ Warm-up epochs validation-selected λProto _Proto, λOT _OT exp([−4.6,−0.7]) (U[-4.6,-0.7]) Table 5: Best hyperparameters of OT-FlowRec on each dataset. Dataset LR Layers d Drop. Attn Drop. M ODE τ ϵOT _OT Iter. Warm-up λProto _Proto λOT _OT Beauty 5.87×10−45.87×10^-4 1 128 0.39755 0.44607 96 6 0.03919 0.12053 10 12 0.11967 0.02177 Toys 6.322×10−46.322×10^-4 1 256 0.45730 0.26735 96 6 0.02318 0.117279 10 12 0.056853 0.02742 Video_Games 6.30×10−46.30×10^-4 2 128 0.49551 0.340265 96 6 0.084436 0.081655 5 9 0.12009 0.05440 Appendix E Additional Experimental Results Validation curves corroborate these conclusions from the perspective of optimization dynamics. As Figure 6 illustrates, the full model achieves more stable and higher validation N@20 scores across the Beauty, Video Games, and Toys datasets. On the Toys dataset, the full model converges faster during early training and maintains its lead in later stages, indicating that multi-interest modeling and optimal-transport bridge paths more effectively capture the evolution of user interests. Curves for the Video Games dataset exhibit more pronounced fluctuations, reflecting its more complex user interests and item semantics. While the full model maintains optimal performance in later stages, removing the OT-MBFM module causes frequent oscillation and insufficient convergence. This demonstrates that OT-MBFM not only improves final recommendation accuracy but also alleviates directional conflicts during training, yielding a more stable optimization trajectory. Although performance gaps among variants are smaller on the Beauty dataset, the full model still performs best. This suggests that the marginal benefits of individual modules diminish when user interest structures are smooth, whereas the advantages of the optimal-transport-guided multi-bridge flow mechanism become more prominent on datasets with diverse interests and complex semantics. The training curve for the w/o PTW variant highlights the core contribution of PTW in aligning continuous distribution fitting with practical ranking metrics. By progressively adjusting the beta distribution bias for time-step sampling, PTW dynamically biases optimization weights toward the final states of the generation process, rather than relying on balanced full-path supervision. During early training stages, this variant still exhibits an upward trend comparable to the full model, suggesting that the basic optimal-transport bridge flow alone can learn effective directions for interest evolution. In later stages, however, it frequently plateaus or oscillates, failing to reliably achieve the optimal validation N@20 of the full model. This performance gap is especially evident on the Video Games and Toys datasets, where the full model maintains a distinct lead. These findings confirm that without dynamically biasing weights toward the final states of the evolution process, the model captures the overall transport path but struggles to refine the local discriminative capability required for practical top-k ranking. Figure 6: Validation N@20 curves of OT-FlowRec and the ablation variants