Listwise Preference Diffusion Optimization for User Behavior Trajectories Prediction
Authors: Hongtao Huang
Chengkai Huang
Junda Wu
Tong Yu
Julian McAuley
Lina Yao
Venue: NeurIPS 2025 poster ()
Keywords: User Behavior Prediction
Diffusion Models
Primary area: deep_learning

Abstract: Forecasting multi-step user behavior trajectories requires reasoning over structured preferences across future actions, a challenge overlooked by traditional sequential recommendation. This problem is critical for applications such as personalized commerce and adaptive content delivery, where anticipating a user’s complete action sequence enhances both satisfaction and business outcomes. We identify an essential limitation of existing paradigms: their inability to capture global, listwise dependencies among sequence items. To address this, we formulate User Behavior Trajectory Prediction (UBTP) as a new task setting that explicitly models longterm user preferences. We introduce Listwise Preference Diffusion Optimization (LPDO), a diffusion-based training framework that directly optimizes structured preferences over entire item sequences. LPDO incorporates a Plackett–Luce supervision signal and derives a tight variational lower bound aligned with listwise ranking likelihoods, enabling coherent preference generation across denoising steps and overcoming the independent-token assumption of prior diffusion methods. To rigorously evaluate multi-step prediction quality, we propose the task-specific metric: Sequential Match (SeqMatch), which measures exact trajectory agreement, and adopt Perplexity (PPL), which assesses probabilistic fidelity. Extensive experiments on real-world user behavior benchmarks demonstrate that LPDO consistently outperforms state-of-the-art baselines, establishing a new benchmark for structured preference learning with diffusion models.

Listwise Preference Diffusion Optimization for User Behavior Trajectories Prediction
Hongtao Huang*
Chengkai Huang" University of New South Wales and Macquarie University chengkai. huang @unsw. edu. au
University of New South Wales hongtao.. hww.ggunsu. edu. au
Junda Wu
Tong Yu Adobe Research tyužadobe.c com
Julian McAuley University of California San Diego jmcauley@ucsd.edd
University of California San Diego jux0690ucsd.edd edu
Lina Yao
CSIRO's Data61 and University of New South Wales 1ina. yawoynsw. edu. au
Abstract
Forecasting multi-step user behavior trajectories requires reasoning structured preferences across future actions, a challenge overlooked by traditional sequential recommendation. This problem is critical for applications such as personalized commerce and adaptive content delivery, where anticipating a user's complete action sequence enhances both satisfaction and business outcomes. We identify essential limitation of existing paradigms: their inability to capture global, listwise dependencies among sequence items. To address this, formulate User Behavior Trajectory Prediction (UBTP) as a new task setting that explicitly models long- term user preferences. We introduce Listwise Preference Diffusion Optimization (LPDO), a diffusion-basse training framework that directly optimizes structured preferences over entire item sequences. LPDO incorporates a Plackett-Luce su- pervision signal and derives a tight variational lower bound aligned with listwise ranking likelihoods, enabling coherent preference generation across denoising steps and overcoming the independent-tooke token assumption of prior diffusion methods. To rigorously evaluate multi-step prediction quality, we propose the task-specific met- ric: Sequential Match (SeqMatch), which measures exact trajectory agreement, and adopt Perplexity (PPL), which assesses probabilistic fidelity. Extensive experi- ments on real-world user behavior benchmarks demonstrate that LPDO consistently outperforms state-of- the-art baselines, establishing new benchmark for structured preference learning with diffusion models.
Introduction
Understanding and forecasting user behavior is a vital problem in personalized Al and interactive Many approaches, such sequential and dynamic recommendation models, use a user's past interaction sequence to predict the next item or action of interest g
systems 11 2 6
Equal contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

Traditional sequential recommendation models typically focus on predicting a user's next item based on recent history p 10 ... Although this one-step (myopic) approach can capture short-term preferences, it often optimizes immediate engagement metries (e.g. clicks or quick rewards) at the expense of long-term user satisfaction [2 13 In fact, immediate feedback signals offer limited insight into a user's s lasting interests and can even mislead the system. For example, click-based optimization may favor clickbait content that hurts long-term enjoyment 7. As a result, next- item recommenders tend to be short-sighted which optimize only short-term rewards (such as contextual bandits for clicks) can yield suboptimal recommendations in the long run [7]. In summary, one-step sequential models often neglect the longer-term consequences of each recommendation, potentially degrading user experience over time.
greedy. Studies have observed that approaches
In contrast to that, predicting user behavior trajectories goes beyond next-item recommendation by forecasting a user's sequence of future actions across multiple time steps or stages. This can involve predicting user's engagement over a longer horizon (days or weeks ahead), or modeling multi- stage decision processes rather than a single step. By anticipating user behaviors at multiple future timestamps, we can aim to capture longer-term preferences, intentions, and patterns that traditional sequential models might miss. Thus, we introduce User Behavior Trajectory Prediction (UBTP), which challenges model to generate a coherent, ordered sequence of future interactions based on a user's past behavior. Unlike single-step forecasting, UBTP must account for drifting preferences, capture dependencies among successive actions, and manage the compounding uncertainty inherent in multi-step predictions.
Recently, diffusion models have emerged as a powerful paradigm for generative recommendation [5] 16 17), providing a probabilistic framework to systematically model uncertainty and produce diversified recommendations through explicit learning of latent data distributions. However, while current diffusion-basse recommenders demonstrate effectiveness in next-item prediction scenarios, their direct extension to the user trajectory prediction tasks fails to account for the dynamic evolution of user preferences across different temporal stages within predicted trajectories. This limitation leads to compromised prediction fidelity, where the learned plausible distributions may inadvertently incorporate more non-target items due to unmodeled preference transitions as shown in Figure (b)).
Existing diffusion-baard -bsed recommenders typically incorporate point-wise preference signals by ad- justing the likelihood of each item independently during denoising, which encourages the model to favor relevant items at individual positions. However, this approach neglects the joint dependencies and relative ordering among items in the final list, crucial aspects for generating coherent multi-item trajectories, and thus can still scatter probability mass over unrelated targets. In contrast, a list-wise treatment of preference supervision directly maximizes the joint likelihood of the entire ordered list (cf. Figure [ (d)), naturally capturing both item relevance and inter-item relationships.
A natural question arises: can we inject listwise preference supervision directly into the diffusion process to produce more accurate and coherent user behavior trajectories?
We propose Listwise Preference Diffusion Optimization (LPDO), a novel method that aligns the reverse diffusion process with listwise ranking objectives. The standard training objective of diffusion models optimizes variational evidence lower bound (ELBO) with marginal reconstruction losses, but it treats each prediction independently and overlooks the ranking structure that is fundamental to personalized user trajectory prediction. Therefore, we inject Plackett-Luce ranking signal into the variational lower bound, ensuring that at every denoising step the model favors true items over alternatives. This principled integration bridges diffusion denoising and personalized ranking, making the generation process more consistent with the UBTP objective, Compared to non- -i-dfffusion models (cf.. Figure I (a) and traditional diffusion models (cf. Figure (b)). our preference-awe framework (cf. Figure (c)) produces coherent, preference-alignee trajectory generations. Our main contributions are summarized as follows:
We formally define User Behavior Trajectory Prediction (UBTP) as the task of forecasting an ordered sequence of k future user interactions, highlighting its practical importance and challenges.
We propose the Listwise Preference Diffusion Optimization (LPDO), novel training paradigm that seamlessly incorporates Plackett-Luce listwise ranking into the diffusion ELBO, enabling coherent and preference-aware generation of user behavior trajectories.
We propose principled ELBO that incorporates Plackett-Luue ranking terms, tightly coupling diffusion denoising with multi-step ranking likelihoods.

---

Pubabday
Movic Scries
Unrolsted Movies
Prodicted Movie List
ets pesble
pigg
piiig
pilto
Lan
pilly
pilly
(a) Non-OM
(b) Traditional DM
(c) Preference- aware DM1
(4) Positiea- and list-wise optimizatton
Figure 1: Examples of user trajectory predictions and a comparison of optimization strategies. The circles B a # represent series of theme-related movies (e.g.. Harry Potter film series), and the cross indicate unrelated movies that user does not prefer; the dash line + denotes the predicted movie list that user might be interested in; the left color bar shows spatial probability. (a) Non-DM model (e.g., SASRec (T8) is typically deterministic and predict a fixed trajectory, which often fails to capture users' latent preferences. (b) Traditional diffusion model captures preference distribution to produce a more robust trajectory, but the distribution may overlap with unrelated targets. (c) Preference-ate diffusion model incorporates user preference into the sampling process, concentrating the trajectory distribution on related targets and yielding more coherent recommendation lists. (d) Comparison of optimization objectives: position-wise preference optimization (top) independently maximizes each position's 's likelihood and ignores inter-item dependencies; list-wise preference optimization (bottom) maximizes the joint likelihood of the entire ordered list, better capturing ordering and dependencies among items and producing more consistent, accurate behavior trajectories.
We propose the novel Sequential Match (SeqMatch) metric to rigorously evaluate multi-step prediction quality.
On four benehmark datasets, LPDO achieves new state-of-the-arr performance, substantially improving both precision and sequence coherence over other baselines.
2 Related Work.
User Behavior Modeling, User behavior modeling plays an important role in recommender systems. Traditional sequential recommendation models [19 [8 g [0] focus predicting the next item by modeling recent interactions, but they often struggle to capture long-term preferences or multi- step behaviors. Recent approaches forecast user behavior trajectories over multiple time steps or conversion stages. Graph Multi-Scale Pyramid Networks (GMPN) (20) capture multi-resolution temporal dynamics and category dependencies for purchase prediction. The Adaptive Intent Transfer Model (AITM) [12] models sequential dependencies in multi-stage conversion funnels via adaptive feature transfer. PinnerFormer [13] employs a Transformer-bast model to forecast comprehensive user engagements.
Diffusion Models in User Behavior Prediction. Unlike traditional generative models such as VAEs and GANs, diffusion models [21] employ a denoising based generation process that progressively reverses multi-step noising procedure. This approach enables more precise alignment between generated samples and the underlying training data distribution and show promising results in various generative tasks. Recently, diffusion models have emerged as the prevailing generative
predictor in many user behavior modeling tasks [2 23 24 DiffRec (25) proposes the application
of diffusion processes users' interaction vectors (i.c., multi-hot vectors) facilitate collaborative recommendation. DiffuRec [15] uses a Transformer backbone to reconstruct target representations based on the noised user's historical interaction behaviors. DCDR (26) adopts a discrete diffusion framework for progressive re- re-ranking. DreamRec [14] generates oracle next-item embeddings based on user preferences but faces scalability challenges due to the absence of negative sampling. PreferDiff [16] reformulates the BPR loss for diffusion models. DCRec [27] further enhances alignment between generated predictions and user preferences through implicit and explicit conditioning mechanisms. Although promising, these methods are not ideally suited for trajectory prediction due to their position-wised optimization objectives and their disregard for the causal relationships within the predicted trajectory.
3

---

3 Preliminary
In this section, we introduce notation and formally define the tasks studied in this paper. Definition (User Interaction History). Let = ( M } denote the item universe of size M. For each user u, we denote their observed interaction history up to time n as:
H (f.,1 fu.2............................ fu.,) I,
(1)
where fu, the j-th item interacted by user u and n is the history length. Definition 2 (Multi-step Top-K Sequence Prediction). Given a user history H₂ (iu.1...., the goal is to predict the next items:
S_ (fu,++1, hu,, kan+
(2)
in which for each future position j {l,.... k), the model outputs ranked list of K candidates
Anj = (0u5).1,005.2..... (..jkk.......kkk).
such that A I and |Au.il K. The evaluation metrics are based on the inclusion of the
ground-truth item ku,ttj in Au.j.
Objective of Difflusion Models. We first revisit the vanilla diffusion models, established by DDPM 21 and introduce the diffusion objective employed in user behavior modeling. The objective optimization of diffusion parameterized by is to model the distribution of user behaviors, denoted by Po().), where 2p is the target sample. In the context of diffusion based recommendation, 20 corresponds to the embedding of target item
To learn the (zo),, DDPM first progressively add noise to sample žn as , 2T), where T is the number of diffusion steps and 2r standard Gaussian noise. Each step be formulated as g(2a 2e(2z-1) (2r:: Vat2t-1, (1 at I),, where the Gaussian parameters a varies over time step This is called the forward process.
The reverse process is recovering the zo by (ZT...., 20), where each denoising step can be also formulated as a Gaussian transition pa (2)-1 N (z p (u(( Zt, t), (2(2,, t)). Based on the forward and reversed process, the objective optimization based on ELBO can be formulated as:
Calls((z,,)) + log (2(2)))) (is(i]20) 20)
+ log 2 (20)
CELSO (xg(zoer(1)
(4)
(2(2T)
Ciscmsmmation
Cruniias
EReuutrizztion
where is the denoising model and Φ represents the parameters of embedding layers in the recom- mendation task. It is worth noting that & and C; is not included in DDPM as it was originally designed for image domains without embedding layers. We provide a detailed derivation in Appendix I
Diffusion Model Inference and Behavior Modeling, Starting from pure Gaussian noise, diffusion models employ the denoising network fe to iteratively generate latent embeddings, culminating in the inferred behavior prediction embedding 20. This embedding 2n is then mapped back to the corresponding item space. In sequential recommendation tasks, the Top- K items from the candidate set are identified as potential user preferences.
4 Listwise Preference Diffusion Optimization
In this section, we present Listwise Preference Diffusion Optimization (LPDO), novel framework for the UBTP task. LPDO departs from standard diffusion-basse recommenders by directly instilling listwise preference information into non-eevtreeresssvve diffusion model in continuous latent space, coupled with a Plackett-Luce ranking objective. This unified generative ranking design raises several nontrivial challenges: most notably, how bridge the gap between continuous denoising and discrete Top-K K list creation, how to derive a tractable variational bound that jointly accommodates reconstruction and listwise likelihood, and how to balance generation fidelity against preference alignment without destabilizing training. In the remainder of this section, we describe how we overcome these hurdles through (i) an end-to-end differentiable scoring head mapping denoised latents to item logits, (ii) the preference causal transformer, which models the directional dependencies among

---

denoised item representations to capture causal preference order and enhance listwise consisteney and (ii) tight ELBO decomposition that seamlessly integrates Plackett-Luce terms.
Our approach leverages non-autoregressive diffusion model in continuous latent space, combined with Plackett-Luce ranking objective. We describe the key components below.
4.1 Diffusion Framework for UBTP
Objective of Diffusion UBTP. We extend the diffusion optimization framework for trajectory prediction based on DCRee (27] Unlike prior works that add noise solely to the target item embed- ding Zy [14 15 [6] DCRec concatenates the target item embedding with the corresponding history embedding, thereby introducing an explicit conditioning signal through Zo. This concatenation strategy has also been shown to be effective diffusion paradigm in NLP tasks [28]. Motivated by this, we adopt similar design for the UBTP task by concatenating the target trajectory with its corresponding historical context. Let sponding to the future items. The concatenated sample can be formulated as X = concat ( (,. zo]. Therefore, as illustrated in Figure 2] and po (Xt-1 X,, H), respectively, based on which Equation (4) can be extended as follows:
(20,11.... 20.&) ) E &
be the latent embeddings corre-
we reformulate the forward and reverse processes 9X,, (X-1)
Σ Cillfo(X..)) Xoll 2 log To Xo Su.)
+ log ((xr|Xo)
LUSTE Egg (Xa: (Su)
(5)
D& (X)
(x
EReconataction
Eaakin
RResdiicaio
where S,, is predicted item lists corresponding to Zo-
Preference Causal Transformer. Unlike the next-item predic- tion target in previous user behavior tasks, trajectory prediction exhibits strong causality and a clear evolution of user prefer- ences within the trajectory. Therefore, shown in Figure bottom, we employ a causal transformer backbone as fg. The concatenated embedding X, and time embedding are sent to the causal attention layer. Following [27], the clean history embedding Ho is then added as conditioning signal through a cross-attention layer. This model effectively captures causal dependencies and user preferences while denoising the input, thereby enhancing the quality of the generated outputs z.
(K,1))
pracess
H
x
Reverse process
Cross Attention
X
4.2 Bridging Diffusion and Sequential Listwise Ranking
Causal Attention
To ground our sequence-level diffusion objective in established learning-to-rank theory, we begin by recalling the classical Bayesian Personalized Ranking (BPR) loss [29]. which opti- mizes pairwise preferences. Given a user u. a positive item it and negative item i BPR minimizes:
3G,
24
Figure 2: Illustration of LPDO.
CBrn In ar (ū..st U..t
(6)
where Bu, is the predicted score for effective for one-step ranking, BPR has two major drawbacks in our UBTP task: (i) Pairwise myopia: it only compares one positive/negative pair, ignoring interactions among the full future sequence (iu.nt1...., (u,n++)) (ii) Latent-variable mismatch: BPR's pointwise score differences cannot readily incorporate the diffusion latent variables X, that model an entire trajectory each step.
on item and o(.) is the sigmoid function. While
To capture full-sequence structure, we turn to the listwise likelihood framework. Let = |...... TR] be a permutation of the K candidate items at one future position j. ListMLE (30 maximizes:
K LLAMMLE Σ log Eiec, exp(s:)
exp(
(7)
where C- (mT............. 1,
(8)
where is the score for item i, and C denotes the candidate set at this prediction step. This listwise objective jointly enforces consistency among all ranks within the position However, the strict
5

---

exclusion of lower-ranked items can produce overly peaked distributions and sparse gradients that impede stable optimization. Thus, we further loosen ListMLE:
K log (1-?) Eiec, exp(s:) + Eisc exp(s:)
expl
Lsoft-LstMLE
(9)
where 7 E [0, 1] is penalty factor. Building on Lsoft List-LE, we embed listwise ranking into our diffusion-based user trajectory model. Recall from Section 4.1 that we already have:
X concal (H. (f,,1,...,,,, ,.,)))
(10)
We then define a listwise diffusion loss over the ground-truth next-item sequence Su:
Praft In po (hents) X., Hi:7).
(11)
where (o(in, X.. 7) is the Plackett-Luce model when O. In this way, Prat inherits the global ranking advantages of ListMLE while fully integrating the diffusion latent dynamics that generate multi-step user trajectories.
4.3 Derivation of ListPref Loss
To optimize the joint likelihood of the latent trajectories and the Top-K K lists, consider optimizing Equa- tion This objective is directly intractable because requires marginalizing over the full diffusion chain Xa.r. We introduce the forward noising process q(Xorr| Xo) as a variational posterior [1] and obtain:
LristProl Σ
Ia pol polinnntss Xorr 7):) dXo.r
Σ In g(oorr Xo) p(Xr) Ie pa (X X1, H) polbunnts j=1
k
Xo. H::7)
dNo.r
((xoT Xo)
< Eq(Xor))X) (n)) E ln pol pedimnts Xo. Him))
KT X. Xo) po
(X Po
X,,Hi:)) kT(a(Xr Xo) (o(x))
(12)
4.4 Connecting Diffusion Models With Listwise Maximum Likelihood Estimation
4.4.1
Joint Likelihood and ELBO
To formally connect diffusion-basse based generation with listwise maximum likelihood, we write the joint likelihood of the next-item sequence and the diffusion chain:
In Po (fu.nty, Xa. (1) = In po (Xr)
Σ
Hin) + Σ po (fun-;) Xo, Hi7),
(13)
where ps (X,-1 Xx, H:; 7) denotes the reverse diffusion kernel and pa(iu.nt)) Xo, Hin) models the listwise likelihond of the next item under the denoised latent state.
Maximizing the marginal likelihood Σド (fu.n H::) is intractable, it requires integrating over all diffusion trajectories. To address this, introduce the variational distribution g(Xorr Xo) approximate

---

the forward noising process and derive evidence lower bound (ELBO):
f g(Zo.r Xo) Σ 5== Po (funtti No.r His)
In pa (ba,ots
H:r) = In
dXaer
q(xurr Xo)
T Σ
KL ((x,11 X,: Xo) po Xc, Hir))
1=1
h By(Xoo Xo)
In po (dmnts)) Xo. Hir)]
(14)
The derivation details are given in the Appendix
Dropping constants and reordering, the final ELBO becomes:
LELBO = Σ Ix Xo) (X X,, H:n))
Σ B Rx(Xxr In (fu.nts Xo, H: 7)
(15)
Minimizing CELBO jointly optimizes denoising fidelity (first term) and listwise ranking utility (second term). thus bridging diffusion generation with listwise maximum likelihood estimation. provide pseudo-eode of the training process in Appendix [ Please refer to for more details.
4.5 Optimization and Inference
Optimization. We optimize L(0) via stochastic gradient descent. At inference, sample from pe hy iterative denoising from 2n NO, I) down 21, then compute scores $3 and select Top-K per position parallel:
LiPDO
XSsimple
Lxeg
(16)
Reconstraction Loss
Lesrning Preference
Regulurizatinn Loss
Here, Liample and Leeg defined in Equation and listwise ranking fidelity during training.
This unified objective jointly enforces trajectory consistency
Inference. At time, given history Nu, sample k-step future trajectory follows:
Xy ~ (0. I), X,- = no Xx, t) Eo [X,, t) 1/2 ets 6 NNO,, I), t T= 1.
(17)
After obtaining denoised latent X1, we compute for each future position j 1...., the ranking scores:
85, = 2o (x)5s i
(18)
and select the Top-K K items:
A..j Topk (1ss,((sss)k))))
(19)
We also provide pseudo-code for the inference process Appendix Please refer to it for more details.
4.6 Evaluation Metric for UBTP
Commonly used evaluation metrics for next-item prediction tasks, such HR@K and NDCG@R K, well-suited UBTP tasks because they effectively capture the sequential relationships within long-term predictions. Similarly, sequence-basee metrics from NLP tasks, such as BLEU [13] and ROUGE [31], are also inappropriate for UBTP tasks due to their emphasis on strict Top-1 matching, This requirement is challenging to meet in user behavior tasks, where data sparsity significant issue.
To evaluate the long-term prediction ability, inspired by the conventional Top-K metric HR @ K. list- wise metric ScqMatch@e @ (SM@ @ to measure the similarity of trajectories follow:
Seq @
Σ sEDD
(fu.nts Au.s)
(20)
DDesal
where Diss is the test dataset. SeqMatch@ K measures the strict consistency of trajectory prediction model. It calculates the percentage of test trajectories where every target item in the trajectory appears in the model's Top- K predictions for their respective positions. We provides example of SeqMatch @ K in Appendix
7

---

5
Experiments
this section, we aim to answer the following research questions:
RQI: How does LPDO perform on the UBTP task compared to state-of-the-ar baselines?
RQ2: How does LPDO benefits from Luco comparing to other diffusion-based methods?
RQ3: What the impact different hyperparameters (e.g., balance factors À and 7) on LPDO's performance?
RQ4: What are the inference cost and model complexity of LPDO compared to the baseline methods?
5.1 Training Setup
Datasets. We evaluate our approach on three sequential recommendation datasets: Amazon Beauty [2). MovieLens-IM [33] and LastFM [34] We adopt the standard Leuve-One-One Out data-splitting stralegy commonly used in sequential recommendation tasks, where the "One" in our setting refers user trajectory with a predefined sequence length. The trajectory longth is set to 3 for Amazon Beauty, and 5 and 10 for MovicLens- IM and LastFM, respectively. Detailed dataset statistics are provided in Appendix G
Baselines. Since UBTP is newly proposed task, we conduct comprehensive comparison of LPDO against seven representative baselines from sequential modeling. These include three conventional methods: FPMC
[35] SASRec [88) and STOSA [6);; four diffusion-based generative methods: DiffuRee [15. DreamRec (14), PreferDiff 16 and DCRec 2 Among them, all baselines are modified from their default training objectives to support UBTP by applying the loss to each predicted item. Additionally, we extend SASRec to support auto-regressive generation, denoted as SASRec-AR. This variant predicts the next item at each step, appends the predicted item to the input sequence, and then performs the subsequent prediction based on the updated history.
carefully tune their hyperparameters performance on the validation set. For our LPDO, we X=0.1 for all datasets, and 7=0.0/0.3/0.8 for Beauty, MovieLens-11 M and LastFM. We set the number of diffusion timesteps to 50 for training and 1 for inference, and the 3 linearly increases in the range of 1c-4, 0.02). We set the number of candidates K = M during training. All models are trained and evaluated on an NVIDIA RTX 3090 GPU, and the training stopped after S evaluations without improvement prevent overfitting. More implementation details are described Appendix H
Implementation Details. For all baselines.
achieve the best
Evaluation. To evaluate the whole predicted trajectory, modify the HR and NDCG@K K metric, which for next-item prediction, to sequence HR (SeqHRR) and sequence NDCG NDeGN SeqHR and SeqNDCG are sequence-level evaluation metrics that compute the geometric mean of position- -iie HRs or NDCGs. Furthermore, we introduce SeqMatch (see Section[4.6). enforcing strict consistency evaluation across all time steps in trajectory. Meanwhile, also use Perplexity (PPL) (37) to quantify the uncertainty of the predicted trajectory. For numerical stability, PPI. is scaled by applying logarithmic transformation. Following we rank all candidate items for each predicted item the target trajectory.
[5] 38
5.2 Performance Comparison (RQ1)
In this section, Table rreportss the comparison results between our method and 8 different baseline methods on three datasets with three different trajectory length settings. LPDO demonstrates significant improvements across all datasets, highlighting the effectiveness of siffusson-based approach for UBTP tasks. By incorporating listwise preference-aware optimization strategy, our framework facilitates the coherent and accurate generation of user behavior trajectories. This enhancement improves consistency within the diffusion process, which is evidenced by the performance gains over baseline methods.
Moreover, diffusion-based methods with ranking loss, such as DiffuRec and DCRec, generally outperform non-diffusion methods. In contrast, diffusion models without ranking loss. such as DreamRec and PreferDiff, struggle with trajectory prediction tasks, resulting in nearly zero values in all ranking metrics with significantly higher PPL (e.g.. PPL of PreferDiff >500.0). attribute this performance gap to embedding collapse; further analysis appears in Section This trend indicates the advantages of generative modeling techniques and the integration of ranking loss in capturing complex user behaviors and enabling causal future behavior prediction. Among these methods, diffusion based approaches like DiffuRec and DCRec demonstrate superior performance, likely due to their ability capture the inherent uncertainty of user interests. Notably, LPDO surpasses both DiffuRec and DCRee across all datasets, showcasing that the incorporation listwise optimization further enhances the modeling of user preferences in hoth the forward and reverse diffusion processes.
5.3 Benefit From LLPDO (RQ2)
In Section 4.4 we discuss how LPDO handles high-ranking items with larger gradients. Empirically, we find that there are two main advantages.
8

---

Table 1: Overall performance comparison across different datasets and trajectory length settings.
Data
Metric
FPMC
SASRec
SASRec-ss
STOSA
DilluRee
DreamRte
PerferDiff
DCRec
LPDO
Improve.
SH@5
0.0236
0,0219
0,0218
0,0238
0.0274
0.0002
0.0025
0,0250
0.0307
12.04%
Beauty
(len=)
SH1@1 10
S
0.0376
0.0129
0.0466
00114
0.0455
0.0114
0.0120
0.0407
0.0442
0.0149
0.0006
0.0001
0.0015
0.0055
0.0388
0.0135
0.0503
0,0164
10.07%
7.94%
SN@ 10
0.0158
0.0199
0.0195
0.0171
0.0188
0.0003
0.0025
0.0159
0.0248
24.62%
SM@50
0.0253
0,0257
0.0238
0.0177
0.0363
0.0000
0.0000
0,0432
0.0521
20.60%
PPL
37,56
51.25
52.59
54,89
36.89
89,55
> 500.0
38.90
33.86
8.21%
S
0.0157
0.0895
0.0795
0.0865
0.0894
0.0028
0.0004
0.1
0.1218
10.03%
ML- IM
5len5))
S 10
0.0371
0.1365
0.1366
0,1476
0.1540
0,0054
0.0165
0,1823
0.1983
8.78%
SN@5
0.0098
0,0434
0,0445
0.0493
0,0506
0.0016
0.0049
0.0621
0.0679
9. 3,34%
SN@ 10
0.0179
0,0573
0.0574
0,0627
0.0649
0.0023
0.0073
0.0759
0,0825
8. 70%
SM 50
0.0160
0.1045
0.1049
0.1074
0.1168
0,0000
0.0000
0.1458
0.1559
6.92%
PPL
38.43
33.62
33.58
33.47
32.47
165.59
> 500.0
31.42
30.36
3.37%
S
0.0058
0.0581
0.0560
0.0476
0,0624
0.0022
0.0077
0.0717
0.0819
14.22%
ML. IM
(len= 10)
10@
0.0140
0,1033
0.0985
0.0864
0.0043
0.0101
0.1277
0.1419
11.12%
S5@5
0.0036
0.0331
0.0320
0.0276
0,0356
0.0012
0.0043
0.0412
0.0461
11.89%
S
0.0068
0,0446
0.0426
0.0377
0.0456
0.0018
0.0006
0,0550
0.0603
9.63%
SM@-50
0.0000
0,0299
0.0261
0,0214
0.0311
0,0000
0,0000
0.0381
0.0447
17.32%
85.55
68.99
70.41
73.92
68.35
305.19
> 500.0
68.58
67.44
1.66%
SH@5
0.1636
0.1816
0.1829
0.1537
0.1793
0.0433
0.0035
0.1931
0.2507
29.83%
SH@ 10
0.2311
0.2523
0.2564
0.2184
0,2458
0.0531
0.0065
0.2681
0.3244
26.52%
Last-FM
(len=5)
SN@5
0.0830
0.0917
0.0908
0.0760
0.0906
0.0205
0.0023
0.0972
0.1260
29.63%
SN@
0.0897
0.0953
0.0972
0.0836
0,0921
0.0185
0.0028
0.1015
0.1195
17.73%
SM@50
0.1636
0.1578
0.1636
0,1463
0.1638
0.0189
0.0000
0.1723
0.2357
36.81% %
PPL
39.29
28.26
28.20
30.65
30,5495
149.98
> 500.0
29.28
27.28
3,26%
SH@5
0.1080
0.1163
0.1148
0,0888
0,1209
0,0290
0.0000
0.1311
0.1705
30.05%
Last-FM
(len= 10)
SH 10
0.1703
0,1606
0.1654
0,1495
0.1715
0.0407
0.0074
0.1881
0,2362
25.57%
SN@5
0.0598
0.0608
0.0597
0.0471
0,0625
0,0141
0.0000
0.0673
0.0879
30.61 %
SN 10
0.0686
0.0610
0.0645
0,0624
0,0665
0.0159
0.0033
0.0730
0,0889
21.78%
5@:50
0.0713
0.0635
0.0566
0.0449
0,0586
0.0098
0.0000
0.0557
0.0762
6.87%
PPL.
83.16
61.69
61.56
66.41
65.29
283.50
500.0
61.32
60.93
0.64%
SIt@ SN@K, and SM@K denote SK SeqNDCG@K and SegMatcheK. respectively. For all metrics except PPL. higher values indicate better performance. Bold results indicate the hest results, while undertined results denote the second-hest hest. fnpprsee denoles the relative improvement of LPDO over the strongest baseline. The improvements are statistically signilicant (y < 0.05). For detailed performance comparison with more metrics, please refer to Appeadix [
Faster convergence. LPDO converges faster than other diffusion- based models employing different ranking losses. As illustrated in 3 LPDO converges within approximately 25 epochs, whereas its counterpart DCRec, which adopts a cross-entropy ranking loss, requires around 33 epochs to reach convergence.
Higher position-wise performance. Figure (b) provides position-wise comparison of SASRec, DiffuRec, and LPDO on trajectory prediction tasks. The x-axis represents the different positions of the trajectory. and the y-axis represents the prediction accurate measured by HR@5 The shaded areas represent the standard deviation. The results clearly show that LPDO consistently achieves higher HR@5 @5 scores across all prediction positions compared to the other methods, indicating its superior ability to capture causal dependencies and the evolution of user preferences over time. Notably, LPDO exhibits a significant performance advantage, particularly at earlicr positions, further highlighting its effectiveness in UBTP tasks.
5.4 Ablation Study of Hyperparameters in LPDO (RQ3)
discuss the deviation of the objective of LPDO. The hyperparameter controls the balance between visiting items in the earlier positions of the trajectory and the remaining items the pool. Figure (c) illustrates the relationship hetween different 7 settings and the model performance on MovieLens- IM dataset. The results indicate that LPDO achieves optimal performance when 7 = 0.3. underscoring the importance of capture user's preference evolution.
Penalty factor y. In Section 4.2
Loss ratio A. In Equation (6).. hyperparameter X controls the balance between reconstruct the trajectory from noise and preference-aware ranking in LPDO. Figure (d) shows that setting À 0.1 achieves an appropriate balance between these two objectives. We also evaluate the distinct contributions of different loss components Lrisree, Liiple. Leeg in MovieLens- IM and LastFM, with trajectory length 5. The results are depicted in T and we can find that: (1) The model collapses completely when removing Liishee achieving zero values in all ranking metrics with significantly higher PPL. This demonstrates the essential role of ranking loss in maintaining basic prediction functionality.
(2) Removing Lsimpl causes severe performance degradation, particularly on MovieLenns- M where SeqHR @5 drops by 53.8%, indicating the diffusion reconstruction loss critically stabilizes the learning process. (3) Omitting Legz results in suboptimal performance, indicating that regularization plays a crucial role in the diffusion optimization process.
Model Backbone. We further conduct an ablation study on the Transformer backbone used in LPDO. Please refer to Appendix for detailed results and analysis.
9

---

6.18
6.31
SeqMatchhgS SegMatchigh 100
0.30
SegMutchhe
UCO
0.25
0.32
0.20
0.11
SaqMarchase
0.36
0.10
0.00
035
0.34
PCfec
0.40
0.00
20
46
0.67
Ps 1 Pos Pes Pos Pes
0.2
0.4
0.8
1.0
0.50
0.10.00
Epoch
Trajectory Prediction
(4) Training process comparison
(b) Position-wise comparison
(6) Study penalty factor y
(d) Study loss ratio
Figure Ablation and analysis of LPDO on ML-IM (len=5) dataset. (a) Training process comparison
between LPDO and DCRec, showing faster convergence and higher Seq @ 50 for LPDO. (b) Position-wis wise comparison of HR @5 across different models, where LPDO consistently outperforms SASRec and DiffuRec at each position of the predicted trajectory. (c) Impact of penalty factor y of
LTaal (d) Effect of loss ratio X, indicating the best performance is achieved at moderate values of
Table 2:
Ablation study of different optimization components in LPDO.
Moviel.ens-IW (len=5)
LastEM (len=S)
Model
S 5t
SegMatch@501
PPL.
SogNDCG@5t @5q
SogMatch@501
PPL
wfo-Crivand
0.0000
0.0000
0.0000
76.54
0.0000
0.0000
0.0000
37.36
wlo- wfo-Csimpl
0.0563
0.0321
0.0370
34.11
0.1452
0.0734
0.1345
29.52
wfo-Lnng
0.0646
0.0366
0.0634
32.99
0.2284
0.1173
0.2123
27.87
CUDO
0.1218
0.0678
0.1567
30.35
0.2507
0.1260
0.2357
27.28
6
Model Inference Cost and Complexity Analysis (RQ4)
In this section, analyze the inference cost and model complexity of LPDO. We evaluate LPDO against baseline models on MovieLens-Ih 1M dataset with trajectory lengths and 10, as summarized Table The inference time for the length-5 setting is generally higher than that for length-10, 10, primarily due to the larger data volume (sce Table 5). Notably, the number of denoising steps in LPDO can be flexibly adjusted, allowing the model to remain effcicntt for real-time trajectory prediction tasks. Although reducing the number of denoising steps may slightly decrease performance, it substantially lowers computational cost. The overall model complexity remains comparable across methods, as they employ a similar Transformer-basee backbone.
Table 3: Comparison of prediction performance with inference cost and complexity.
MovieL.ns- IM (len=5)
MovieLens- 1M (len=10)
Model
Complexity
Time Cost
SeqMatch@501
PPL
Time Cost.
SeqMatch@500
PPL.
SASRee
3.34s
0.1047
33.62
3.29s
0.0299
68.99
O(nd + dn?)
SASRec-AR
4.01s
0.4099
33.52
5.30s
0.0261
70.41
O(dde + dn?)
DiffuRec
24.68s
0.1168
32.47
21.51s
0.0311
68.35
O(nd? + dn?
DCRcc
12.83s
0.1458
31.42
11.18s
0.0381
68.58
O(nd + )
LPDO (Step=1)
3.40s
0.1559
30.36
3.34s
0.0447
67.44
O(nd + dn?)
L.PDO (Step=5)
4.14s
0.1569
30.36
4.07s
0.0446
67.43
Olnde + dn?)
LPDO (Step=25)
8.01s
0.1575
30.35
7.65%
0.0450
67.43
Ond + du?
LPDO (Step=50)
13.46s
0.1575
30.35
12.26s
0.0452
67.43
O(nd + dn
All results are measured by an NVIDIA RTX 3090 GPU, di and n are the represcutation dimension and sequence length, respectively.
7 Conclusion
this paper, we introduced the task of User Behavior Trajectory Prediction, which goes beyond next-item recommendation by forecasting coherent, ordered sequenees of future user actions. To address the inability of existing diffusion-based predictors to capture global listwise dependencies, we proposed Listwise Preference Diffusion Optimization (LPDO), novel framework that seamlessly integrates a Plackett-Luce ranking signal into the diffusion ELBO. We derived tight variational lower bound that couples reconstruction fidelity with listwise ranking likelihood, we presented SeqMatch, trajectory- metric rigorous multi-step evaluation. Experiments on worldw datasets show that LPDO offers consistent improvement in accuracy, sequence coherence, and uncertainty estimation, with practical convergence rate. In future work, we plan to incorporate richer context features, extend to longer trajectories, and explore other sequential decision tasks.
10

---

References
[1] Lin Ning, Luyang Liu, Jiaxing Wu, Neo Wu, Devora Berlowitz, Sushant Prakash, Bradley Green, Shawn O' O'Banion, and Jun Xic. User-llm: Efficient LLM contextualization with user embeddings. In Companion Proceedings of the ACM on Web Conference 2025, pages 2219-1223. ACM, 2025.
[2] Chengkai Huang, Hongtao Huang, Tong Yu, Kaige Xie, Junda Wu, Shuai Zhang, Julian J. McAuley, Dietmar Jannach, and Lina Yao. A survey of foundation model-powered recommender systems: From leature-based, generative to agentic paradigms. CoRR, abs/2504. 164200, 2025.
[3] Chengkai Huang. Tong Yu, Kaige Xie, Shuai Zhang, Lina Yao, and Julian McAuley, Foundation models for recommender systems: A survey and new perspectives. CoRR, abs/2402. 1143, 2024.
[4] Chengkai Huang, Junda Wu, Yu Xia, Zixu Yu, Ruhan Wang, Tong Yu, Ruiyi Zhang, Ryan A. Rossi, Branislav Kveton, Dongruo Zhou, Julian J. McAuley, and Lina Yao. Towards agentic recommender systems in the era of multimodal large language models. CoRR, abs/2503. 16734, 2025.
[5] Yunrui Zhang, Gustavo Batista, and Salil S Kanhere. Instance-wise monotonic calibration by constrained transformation. arXiv preprint arXiv:2507.06511 2025.
[6] Yunrui Zhang, Gustavo Batista, and Salil Kanhere. Label shift estimation with incremental prior update. In Proceedings of the 2025 SIAM International Conference on Data Mining (SDM), pages 134-142. 142. SIAM, 2025.
[7] Ziru Liu, Shuchang Liu, Zijian Zhang, Qingpeng Cai, Xiangyu Zhao, Kesen Zhao Lantao Hu, Pong Jiang, and Kun Gai. Sequential recommendation for optimizing both immediate feedback and long-term retention. In Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 1872-1882, 2024.
[8] Shoujin Wang, Liang Hu, Yan Wang, Longbing Cao, Quan Z. Sheng, and Mehmet A. Orgun. Sequential recommender systems: Challenges, progress and prospects. In Proceedings of the 28th International Joint Conference on Artificial Intelligence, pages 6332-6338, 2019.
[9] Chengkai Huang, Shoujin Wang. Xianzhi Wang, and Lina Yao. Dual contrastive transformer for hierarchical preference modeling sequential recommendation. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 99-109. ACM, 2023.
[10] Chengkai Huang. Shoujin Wang, Xianzhi Wang, and Lina Yao. Modeling temporal positive and negative excitation for sequential recommendation. In Proceedings of the ACM Weh Conference 2023, pages 1252-1263. ACM, 2023.
[11] Guanglin Zhou, Chengkai Huang, Xiaocong Chen, Xiwei Xu, Chen Wang, Liming Zhu, and Lina Yao. Contrastive counterfactual learning for causality-aware interpretable recommender systems. In Proceedings of the 32nd ACM International Conference Information and Knowledge Management, pages 3564-3573. ACM, 2023.
[12] Dongbo Xi, Zhen Chen, Peng Yan, Yinger Zhang, Yongchun Zhu, Fuzhen Zhuang, and Yu Chen. Modeling the sequential dependence among audience multi-step conversions with multi-task learning in targeted display advertising. In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3745-3755. ACM, 2021.
[13] Nikil Pancha, Andrew Zhai, Jure Leskvee, and Charles Rosenberg. Pinnerformer: Sequence modeling user representation at pinterest. Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pages 3702-3712. ACM, 2022.
[14] Zhengyi Yang, Jiancan Wu, Zhicai Wang, Xiang Wang. Yancheng Yuan, and Xiangnan He. Generate what you prefer: Reshaping sequential recommendation via guided diffusion. In Proceedings of the Advances in Neural Information Processing Systems, 2023.
[15] Zihao Li, Aixin Sun, and Chenliang Li. Diffuree: A diffusson model for sequential recommendation. ACM Trans. Inf. Syst., 42(3):66:1-66:26 2024.
[16] Shuo Liu, An Zhang, Guoqing Hu, Hong Qian, and Tat-Seng Chua. Preference diffusion for recom- mendation. In Proceedings of the Thirteenth International Conference on Learning Representations. OpenReview.net, 2025.
[17] Xiaoxin Ye, Chengkai Huang, Hongtao Huang, and Lina Yao. Beyond negative transfer: Disen- tangled snerencce-guide diffusion for cross- dros--domain sequential recommendation. arXiv preprint arXiv:2509. 00389, 2025.

---

[18] WaaggCChngg Kang and Julian J. McAuley. Self-attentive sequential recommendationn. In IEEE International Conference on Data Mining, pages 197-206. IEEE Computer Society, 2018
[19] Balázs Hidasi, Alexandros Karatzoglou, Linas Baltrunas, and Domonkos Tikk. Session based recommen- dations with recurrent neural networks. In Proceedings of the 4th International Conference Learning Representations, 2016.
[20] Chao Huang, Xian Wu, Xuchao Zhang, Chuxu Zhang. Jiashu Zhao, Dawei Yin, and Nitesh V. Chawla. Online purchase prediction via multi-scale modeling of behavior dynamies. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 2613-2622. ACM.
[21] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In Proceedings of the Advances in Neural Information Processing Systems, 2020.
[22] Ting- Ruen Wei and Fang. Diffusion models in recommendation systems: A survey. arXiv preprint vrXiv:2501.10545 2025.
[23] Ling Yang, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Wentao Zhang, Bin Cui, and Ming- Hsuan Yang. Diffusion models: A comprehensive survey of methods and applications. ACM Computing Surveys, 56(4): 105::00330 2024.
[24] Xiaoxin Ye, Chengkai Huang, Hongtao Huang, and Lina Yao. Gaussian mixture flow matching with domain alignment for multi-domain sequential recommendation, 2025.
[25] Wenjie Wang. Yiyan Xu, Fuli Feng. Xinyu Lin, Xiangnan He, and Tat-Seng Chua. Diffusion recommender model. In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 832-841, 2023.
[26] Xiao Lin, Xiaokai Chen, Chenyang Wang. Hantao Shu, Linfeng Song, Biao Li, and Peng Jiang. Discrete conditional diffusion for reranking in recomennatiin. In Companion Proceedings of the ACM on Web Conference 2024, pages 161-169. ACM, 2024.
[27] Hongtao Huang, Chengkai Huang, Tong Yu, Xiaojun Chang, Wen Hu, Julian McAuley, and Lina Yao. Dual conditional diffusion models for sequential recommendation. Proceedings of the 19th ACM International Conference on Web Search and Data Mining, 2025.
[28] Shansan Gong, Mukai Li, Jiangtao Feng. Zhiyong Wu, and Lingpeng Kong, Diffuseq: Sequence to sequence text generation with diffusion models. In Proceedings the Eleventh International Conference on Learning Representations, 2023.
[29] Steffen Rendle, Christoph Freudenthaler, Zeno Gantner, and Lars Schmidt- Thiimm. BPR: bayesian personalized ranking from implicit feedback. Proceedings of the Twenty-Fifih Conference on Uncertainty in Artificial Intelligence, pages 452-461. AUAI Press, 2009.
[30] Fen Xia, Tie- Yan Liu, Jue Wang. Wensheng Zhang, and Hang Li. Listwise approach learning to rank: theory and algorithm. In Proceedings of the 25th international conference on Machine learning, pages 199--1199 2008.
[31] Jianghao Lin, Jiaqi Liu, Jiachen Zhu, Yunjia Xi. Chengkai Liu, Yangtian Zhang, Yong Yu, and Weinan Zhang. A survey on diffusion models for recommender systems. arXiv preprint arXiv:2409.0500 2024.
[32] Julian J. McAuley, Christopher Targett, Qinfeng Shi, and Anton van den Hengel. Image-based recommen- dations on styles and substitutes. In Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval, pages 43-52, ACM, 2015.
[33] F Maxwell Harper and Joseph A Konstan. The movielens datasets: History and context. ACM Transactions on Interactive Intelligent Systems, 5-4): 20155
[34] Thierry Proceedings of the 12th International Conference on Music Information Retrieval, 2011.
Daniel P.W. Ellis, Brian Whitman, and Paul Lamere. The million song datasct. In
[35] Steffen Rendle, Christoph Freudenthaler, and Lars Schmidt- Schmidt-Thieme. Factorizing personalized markoy chains for next- basteb recommendation. In Proceedings of the 19th international conference on World wide web, pages 81 1- 1200002222222 2010.
[36] Ziwei Fan, Zhiwei Liu, Yu Wang, Alice Wang, Zahra Nazari, Lei Zheng, Hao Peng, and Philip S Yu. Sequential recommendation via stochastic self- attentonnn In Proceedings of the ACM web conference 2022, pages 2036 2047, 2022.
12

---

[37] Alec Radford, Jeffrey Wu, Rewon Child, David Luan, Dario Amodei, llya Sutskever, et al. Language models unsupervised multitask learners. OpenAl blog. 188)9, 2019.
[38] Walid Krichene and Steffen Rendle. On sampled metrics for item recommendation. In Proceedings of the 26th ACM SIGKDD international conference knowledge discovery and data mining, pages 1748-1755 2020.
[39] Calvin Luo. Understanding diffusion models: A unified perspective. arXiv preprint 17779 2022.
[40] Xiang Lisa Li, John Thickstun, Ishaan Gulrajani. Perey Liang, and Tatsunori B. Hashimoto. Diffusion-Im improves controllable text generation. In Proceedings of the Advances Neural Information Prucessing Systems 35: Annual Conference on Neural Information Processing Systems, 2022.
[41] Jonathan Ho and Tim Salimans. Classifier-free free diffusion guidance. arXiv preprint arXiv:2207.1259: 2022.
[42] Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. Proceedings of 3rd International Conference on Learning Representations, 2015.
[43] Jiyy Li, Hanyu Li, Zhiyu He, Weizhi Ma, Peijie Sun, Min Zhang, and Shaoping Ma. Rechorus2. A modular and tlsk-flexible recommendation library. In Proceedings of the 18th ACM Conference on Recommender Systems, pages 454 464, 2024.
[44] Jacob Devlin, Ming-Wes Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep bidi- rectional transformers for language understanding. In Proceedings of the 2019 conference of the North American chapter the association for computational linguistics: human language technologies, pages 4171-4186, 2019.
[45] Colin Raffel, Noam Shazcer, Adam Roberts, Katherine Lec, Sharan Narang, Michael Matena, Yanqi Zhou, Wei Li, and Peter Liu. Exploring the limits of transfer learning with unified text-to-text transformer. Journal of machine learning research, 21(140):1 67, 2020.
[46] Xingzhuo Guo, Junwei Pan, Ximei Wang, Baixu Chen, Jie Jiang, and Mingsheng Long. On embed- ding collapse when scaling up recommendation models. Proceedings of the Forty-first International Conference on Machine Learning. OpenReview.net, 2024.
13

---

NeurIPS Paper Checklist
1. Claims
Question: the main claims made the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: Please refer to Section 1
Guidelines:
The answer NA means that abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match thcorctical and experimental results, and reflect how much the results can be expected to generalize other settings.
is fine to include aspirational goals as motivation long it is clear that these goals are not attained by the paper.
2. Limitations
Question: Does paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
Please refer to Appendix A
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper limitations, but those are not discussed the paper.
The authors are encouraged create separate "Limitations" scction their paper.
The paper should point out any strong assumptions and how robust the results these assumptions (e.g.. independence assumptions, noiseless settings, model well well-specificnn specification. asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
violations of
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets with few runs. In general, empirical results often depend implicit assumptions, which should he articulated.
The authors should reflect the factors that inffuence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to text system might not be used reliably to provide closed captions for online lectures because fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an important role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [Yes]
Justification: Please refer to Section 4 Appendix
B
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross-referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
14

---

The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by
formal proofs provided in appendix supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
Experimental Result Reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: Please refer to Appendix G and Section 5.1
Guidelines:
The answer NA means that the paper does not include experiments.
the paper includes experiments, answer to this question will not be perceived well by the reviewers: Making the paper reproducible important, regardless whether the code and data are provided or not.
the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on contribution, reproducibility can be accomplished various ways. For example, if the contribution is novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access the model. In general. releasing code and data often one good way accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to hosted model (c.g., in the case of a large language model), relcasing of model checkpoint, or other means that appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submissions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) If the contribution is primarily new algorithm, the paper should make it clear how to reproducc that algorithm.
(b) the contribution is primarily a new model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution a new model (c.g., a large language model), then there should either be a way to access this model for reproducing the results a way to reproduce model (e.g.. with an open-source dataset or instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors welcome to describe the particular way they provide closed-source source models, it may be that access to the model is limited some way (c.g., to registered users), but it should be possible for other researchers to have some path to reproducing verifying the results.
reproducibility. In the case of
Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, described in supplemental material?
Answer: [No]
Justification:
The entirety of the data in this paper is publicly available. We are unable to include the code due to policy considerations; however, all relevant implementation information is presented in the paper ensure reproducibility.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurIPS code and data submission guidelines httape::/nips.cc/ppllee
Sriide//CoeeSule httpee//oooeeeiiiiiioooooo.....o
for more details.
While we encourage release of code and data, we understand that this might not possible,
so "No" is an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g.. for a new open-soure benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https: : //t/://nipp cc/public/ ou..dess/CooeeSutnleesssoooooo.. for more details.
15

---

The authors should provide instructions on data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only a subset of experiments are reprodueible, they should state which ones are omitted from script and why.
At submission time, to preserve anonymity, authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended to the paper) recommended, but including URLs to data and code is permitted.
Experimental Setting/Details
Question: Does the paper specify all the training and test details (e.g.. data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary understand the results?
Answer: [Yes]
Justification: Please refer to Section 5.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to level of detail that is necessary appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, supplemental material.
7. Experiment Statistical Significance
Question: Does the paper report bars suitably and correctly defined other appropriate informa- tion about the statistical significance of the experiments?
Answer: [No]
Justification: The observed improvements in performance are statistically significant (p < 0.05),
confirming the effectiveness of the proposed approach.
Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.
The factors variability that the error bars are capturing should be clearly stated (for example, train/test split, initialization, random drawing of some paramcter, or overall run with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to library function, bootstrap, etc.)
The assumptions made should be given (e.g., Normally distributed errors).
It should be clear whether the error bar is the standard deviation the standard error of the mean.
is OK report I-sigma enror bars, but one should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors not verified.
For asymmetric distributions, the authors should be careful not to show in tables or figures
symmetric error hars that would yield results that are out of range (c.g. negative error rates).
error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures or tables in the text.
Experiments Compute Resources
Question: For each experiment. does the paper provide sufficient information the computer resources (type of compute workers, memory, time exccution) needed reproduce the experiments?
Answer: [Yes]
Justification: Please refer to Section 5.1
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.
16

---

The paper should provide the amount of compute required for each of the individual experimental well estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn 't make into the paper).
9. Code Of Ethics
Question: Does the research conducted the paper conform, every respect, with NeurIPS Code of Ethics hattpa:/nneurppl https////eerrpp..ccaaca/e////eee wtw.:/eiinncciiiiiieeeeee
Answer: [Yes]
Justification: No ethical issues involved.
Guidelines:
The answer NA means that the authors have not reviewed the NeurlPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that roquire a deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws regulations in their jurisdiction).
10. Broader Impacts
Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
Answer: [NA]
Justification: This paper only focuses on the research task of user behavior prediction and diffusion models on public dataset.
Guidelines:
answer means that there is no societal impact of work performed. the authors answer NA or No, they should explain why their work has societal impact or why the paper does not address societal impact.
Examples negative societal impacts include potential malicious or unintended uses (e.g.. disinformation, generating fake profiles, surveillance). fairness considerations (e.g.. deploy- ment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point out. For example, the quality generative models could used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
legitimate to point out that an improvement in
The authors should consider possible harms that could arise when the technology is being used intended and functioning correctly, harms that could arise when the technology is being used intended but gives incorrect results, and harms following from (intentional unintentional) misuse the technology.
there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitor- ing misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of MI.).
11. Safeguards
Does the paper describe safeguards that have been put in place for responsible release of data models that have high risk for misuse (e.g.. pretrained language models, image generators, scraped datasets)?
Question:
Answer: [NA]
Justification:
The date and models used the experiment are all open source or reproduced by ourselves.
Guidelines:
The answer NA means that the paper poses no such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines restrictions access the model implementing safety filters.
17

---

Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but encourage authors take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators original owners of assets (e.g., code, data, models), used in the paper, properly credited and the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
Justification: Please refer to Section S
Guidelines:
The answer NA means that the paper does not existing assets.
The authors should cite the original paper that produced the code package or dataset.
The authors should state which version of the asset is used and, if possible, include a URL.
The name of the license (c.g., CC-BY 4.0) should be included for cach asset. scraped from particular source (e.g.. website), the copyright terms of service of that source should provided.
assets are released, the license, copyright information, and terms of use the package should be provided. For popular datasets, paperswi thcode. www.coom//aaac /attttttstts has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.
For existing datasets that are re-per re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided.
this information not available online, the authors are encouraged to reach out to the asset's creators.
13. New Assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer: [NA]
Justification: This paper does not release new assets.
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the datasct/code/model as part of their sub- missions via structured templates. This includes details about training, license, limitations,
The paper should discuss whether and how consent was obtained from people whose asset is used.
At submission time, remember to anonymize your assets (if applicable). You can either create an amonymized URL or include anonymized zip file.
14. Crowdsourcing and Research with Human Subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification: This paper does not involve crowdsourcing nor research with human subjects.
Guidelincs:
The answer NA means that the paper does not involve crowdsourcing research with human subjects.
Including this information in the supplemental material is fine, but if the main contribution of the paper involves human subjects, then as much detail as possible should included the main paper.
According to the NeurIPS Code of Ethics, workers involved data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional Review Board (IRB) Approvals Equivalent for Research with Human Subjects
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Question:
18

---

Answer:
[NA]
Justification:
This paper does not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer means that paper does not involve crowdsourcing nor research with human subjects.
Depending on the country in which research is conducted, approval (or equivalent) may be required for any human subjects research. If you ohtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors adhere to the NeurIPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applica- ble), such the institution conducting the review.
19

---

Supplementary Material
A Limitation
Firstly, LPDO depends on manually tuned syperppraneeees--seiiieeett the loss ratio and penalty factor ", to balance reconstruction and ranking objectives. While we show stable results across moderate values of these parameters (Section 5.1 automated adaptive tuning strategies could further reduce human effort and improve robustness. Secondly, evaluation focuses Top- K ranking metries (SeqHR, SeqNDCG) and strict trajectory matching (SeqMatch). These offline metrics may not fully capture user satisfaction or long-tern teg-term engagement live settings. Future work should investigate additional measures, such as personalized utility scores or online A/B tests, to assess real-world impact.
B Optimization Deviation of Diffusion Models
B.1 Diffusion Models for Continuous Domains
A generative model is expected to SeqMatch estimation distribution po to the ground truth distrihution p(z)) as closely as possible, where 9 represents learnable parameters and 2p RR is set of samples. For vanilla diffusion models continuous domains, they model the sample 2o as a Markov chain with sequence of latent variahles {ar,.... 21, =0}, where 27 is standard Gaussian, and each variable is in TRdd. By this means, the latent dimension is exactly equal to the data dimension of 2o. and the diffusion model progressively recovers 20 from Gaussian noise. Each denoising transition 2, 2 is parameterized by linear Gaussian transition pe |a)) (2 1: pe (2x, f), Ea (Zx, f)), calculated by a denoising DNN model [z l). Therefore, joint distribution of diffusion models can be written as:
T
pa pa(zo:) = po(2r) II
(21)
1=1
poeere,p(2z)) (22r;
(22)
To train the denoising model fo(ze, t). diffusion models first construct a progressive noising process -0,.-..22-1,,777 2r), known as the forward process. Corresponding to this, the denoising process is called the reverse process. The forward process adds Gaussian noise to 20 step-by-step until the final latent 27 is linear Gaussian
guaranteed be standard Gaussian. Each noising transition 21-1 - 2: defined transition ( 12) = (aa /Br Iz--1, 8,1), where Gaussian parameters Br varies over time step t. Due to the Markov property and the Bayes rule, the transition can be rewritten with 20 as:
q 1 = ((2)|=x-1.00) 20) 9(2 [e, =0)9(==(=0)
(23)
(#c-1|20)
To optimize the parameter 6, the diffusion model is trained to maximize the log-likelihood of po (2)) according observed samples 20. This objective can be formulated arg max, log ps (20). Mathematically, we can derive a proxy objective called the Evidence Lower Bound (ELBO), a lower bound of the likelihood term log (zo). Formally, the equation of the ELBO is:
Po (2 log
(
(24)
( (2a)
Rather than directly maximizing the likelihood term, diffusion models minimize the minus ELBO as:
log Po po (Zo:T)
arg max log Po (20) ss arg max l
(25)
9
9(#1:T [D))
log ((21 20)
arg min (aser))))
(26)
Po (=(o))))
Combining with Equations and 23 the expectation in Equation
20 can be further derived as:
log ((ar)(z))
log 9(27(20)
T
g(21-1/25 20)
log po(=1-1 [x)) log (zol=a))
(27)
Po (zo:T)
po (ZT)
Therefore, based on Equations
26 and 27 the BasBed optimization object of parameter 0 is to minimise
(22((20)
log 4(=1-1 /2, 20)
Leboo(2) = F. E sa)
log
log log
(28)
po()r)
1|=))
t=2
20

---

To simplify and combine the second and third terms in Equation surrogate objective obtain mean-squared term:
28
recent research [3]
derivative simple
2(2 (z0) pe (err
Latto = (=1
log
Calls(zr,1)) zoll?
(29)
where C₁ is constants associated with timesteps t.
B.2 Discrete Diffusion Models for Discrete Domains in Sequential Recommendation
Motivated by diffusion models in text domains [40,, we extend continuous diffusion models to discrete item domains. Considering discrete item 2 from the item pool 2, the Markov chain in the forward and reverse processes extending {i, ,0, 2T) and (2r,..., 20, i). where i is the discrete item ID. Specifically, map the discrete variables into continuous domains, forward transition process of is defined as (2 i) [zo: Emb(i), 0). where & represents learnable parameters in Emb(i). As for the reverse process, we define the predicted distribution of z as (i) = arg max (2e, Emb (2)), where S is the cosine similarity between 2n and each item embedding of (Z). However, the transition distribution Po (1)20) is implicit.
define a learnable embedding function Emb(.).
Therefore, we extend ELBO Equation (26 to include discrete item as
log (o(2o.)l))
arg max log (i) arg min Byg (sorr(s)
(30)
0.0
Po.o =o:T).
log g0(0)9(2a:r11)
arg min
By (xorl)))
(31)
0.9
po.o 20:T)
And the ELBO-based training objective in Equation
28
is rewritten
Letoo (i) (gg((a (x) log ( (20)
(zool))
Cellfo(z,,t) - 20l1 + log
(32)
(2(T)
pe (1)
There are three terms of objectives in Lano: the prior Meqchtching term Cr, the denoising term L, and the embedding entropy term LH.
The prior Seqchighhig term Lr is similar to the same term in Equation 28 which requires the forward process
transit the 2o into pure noise as the po(=T) is standard Gaussian. Continuous diffusion models (39] omit this term since there are associated trainable parameters. It's worth noting that this term is essential in Calo due the correlation among i, 2g and Φb. This term equivalent to minimizing ||=0|| As the second term La require
fo(z,, f) and close as possible, transfer the objective ||= E folz,, t)1 for fully optimize the DNN models.
embedding entropy term Le can be regarded as KL-divergence Dx ((ol though (2(l))) is a linear transition, the distribution of pa(i)z)) is unknown. Therefore, we replace (gs (()(()z)) by Dxa ((()))))))))) = Da. (a(()))))p))))) The simplified objective of Leto is:
Σ Ofl -2ol)))))))))))) + DRa (90))lps)))))
=all²)
(elbo()
Byg (k))r())
(33)
B.3 Diserete Diffusion Recommender with Historical Conditioning
practice, in the sequential recommendation scenario, the predicted target item relies highly on the user's historical interaction 7 (ho. fu...., ...,.,,,,)) }. where H. C I. Due to the same item pool I, we use the same embedding Emb(i) to map historical conditioning into the continuous domains. Recall that the original reverse transition is parameterized (=
(2, (oa--11/0(00 (a f), Eg t)). Following the conclusion directly incorporate the historical conditioning po (2c-11/2)) Po.0(2c-1122 H) ( Mo.9 Za, t, H), F... Po..(21, H)), where & the learnable parameters of Emb(1), and corresponding denoising model is fo (za, 1, H).
of previous work [11,
Therefore, we rewrite Equation (33) with historical conditioning as:
-2011 =012) +Dal((t))ln(tt))
Amix Lolho (1)
E.g (mq.2r 8)
Σ (1,((es, (1 Call
(34)
21

---

C Derivation of the ELBO for Diffusion Models with Listwise Maximum Likelihood
To formally connect iuffusion-based generation with listwise maximum likelihood, we write the joint likelihond of the next-item sequence and the diffusion chain:
In Io (funtts: X H) = In (X Io (X X,, H)
po (funtt) Xo, H).
(35)
Maximizing the marginal likelihood Σÿ= In paltu.ets H) is intractable due to the integration over all diffusion trajectories. To address this, we introduce the variational distribution (Xa.rr Xn) and derive an evidence lower bound (ELBO):
In po (Pa M) In / g(Xu.r (xo)
Po (o Xo.T H) dXair q(Xu:r
Xu)
2 (x(
(X +
lupe (X.-1 X1, H)
coust.
In po (Juats)
Xu. H)
In (Xarr Xo)
KT KT ((((2 X Xx, po (x.11 Xc. H))
[x Inpo Xo, H)]
(36)
Dropping constants and reordering, the final ELBO becomes:
LELBO Σ KL ((((( X., Xo) (X Xc, {t)
4 Σ B Xo) In (funts Xu, H)]
(37)
Minimizing LELBO jointly optimizes denoising fidelity (first term) and listwise ranking utility (sccond term). thus bridging diffusion generation with listwise maximum likelihood estimation.
D Algorithm
In this section, we provide the pscudo-code of the training and inference process in LPDO.
Algorithm 1 Training
Require: User historical embedding H. target trajectory embedding Zo, number of denoising steps
7. trainable network parameters 0 and embedding parameters é, learning rate
1: repeat
2:
t~ U(1TT), 10,
Sample denoising step and noise.
3:
X, + Concat H. 2n)
D Obtain the concatenated sequence.
4:
X; + vā,X, + vI āie
> Adding noise to X,
5:
0+ 0 - V X,, H:
b Gradient descent update
6:
Φ+ V X,,, H: 0)
Gradient descent update
7: until convergence
8: return optimized 0,
22

---

Algorithm 2 Inference
Require: User historical embedding H. number of denoising steps T,, denoising model fe, target trajectory k, mapping function P
1: XT ~ (0,
> Initialize the model input from Gaussian Noise. > Denoise over T steps Sample noise if not final step.
2: for + T... ...1 do
3: 6 (-, i >> else
4: X0 vou
1 X, VT you (,,
b Denoising. Update step.
5:
X,-1 var-i 10 v 04-16
6: end for
7: 2o - Extract(Xo,h k)
Extract the last item as prediction. >> Mapping from embedding sequence to trajectory.
8: S. - P-poSS..ee 2o)
9: return S.
Predicted Sequence
Target Sequence
Top-1
Top-2
Match
Top-3
pos,
posa
posg
pos,
pos
pos
poss
pos
Figure 4: Illustration of the proposed SegMatch@1 @ N metric. The sequence length is 4 and N N= 3. The icons were generated using OpenAl's ChatGPT. These icons are solely for illustrative purposes.
E Example of Meq @N
Figure provides an example demonstrating how Seq @ evaluates the similarity between predicted and target sequences in the UBTP task. The icons were generated using OpenAl's ChatGPT. These icons are solely for illustrative purposes. At each timestep, the recommender produces k ranked candidate items, forming Top-N matrix. SeqMatch@N checks whether valid trajectory exists that selects candidate per position match target sequence. Unlike traditional item-level accuracy (e.g.. @. NDCG@N) SeqMatch@N measures sequence-level consistency by capturing both order and positional alignment.
F
Case Study
iillustrat a case study user trajectory prediction on MovieLens- the one hand, users may not be interested in certain types of movies. On the other hand, users will also show a decline in interest in the movies they have watched recently. Preference-aware prediction provide users with movie predictions that better conform their preferences.
G Statistics of Datasets
In this section, we provide the statistics of the datasets used in this study, shown in Table Empirically, follow Leave-One-Out rule to split dataset. Specifically, trajectory length only sequences in original datasct with longths greater than + 3 x &e are considered valid. 5 the statistics datasets after processing. The number of items is remaining.
Table 4: Statistics of Datasets.
Dataset
# Sequence
# Items
# Actions
Average Length
Beauty
22,363
12,101
198,502
8.53
MovieLens- IM
6,040
3,416
999,611
165.50
LastFM
891
1,000
1,293,103
1254.49
23

---

Prediction with uninteresled content
Prediction with duplicates
Ideal trajectory prediction
Fandie
Fasl Enight
The Shadew
Fauu Aeader
Tundiia
Regam ta Passden
Next frep, Diems Romane
User Watch History
Preferene-anaree prodiction
Krow Remerca
Nan-Prelonnce prediction
Figure 5: Illustration preference-aware and non-preference prediction on MovieLens- dataset. Due to copyright considerations, we do not show the original movie posters.
Table 5: Statistics of Datasets after Processing.
Dataset
Trajectory Length
Sequence(Before)
# Sequence (After)
Beauty
3
22,363
1927
MovieLens- 1M
5
6,040
6040
MovieLens-Ii 1M
6,040
5231
LastFM
5
891
829
LastEM
10
891
784
H
Implementation Details
We implement all models in PyTorch and adopt consistent training configurations across baselines to ensure fair comparison. For both the baselines and proposed LPDO, fix the embedding dimension to 128 and the dropout rate 0.1. For sequential models, the maximum sequence length is fixed 50. All models are trained using the Adam optimizer 42] with batch size of 256 and a learning rate selected from (0.01, 0.005, 0.001 based on validation performance. For the transformer-bast training is conducted for up to 1,000 epochs with early stopping afler epochs of no improvement. To adapt all models to the UBTP task (i.e., next-k item prediction). modify the output layer predict multiple future items rather than only the immediate next one. Specifically, their training objective reformulated from single-item prediction to trajectory- prediction.
model, the number of blocks is set to 4. Model
Except for the aforementioned configurations, models with public implementations by previous works, including SASRec [18]. STOSA [36), DiffuRec [15), DreamRec [14, and PreferDiff [16), are trained following their respective default settings. For FPMC, we adopt the implementation from ReChorus (3]. For DCRee 27
reproduce the model and its loss halance factor
0.1.
I Ablation Study of the Transformer Backbone
this section, we further analyze the impact different Transformer backbones on the performance LPDO. s presented in Table we compare three variants: the bidirectional Transformer (44) the prefix Transformer [45). and the causal Transformer [37] The results demonstrate that the causal Transformer achieves the best performance, suggesting that its architecture aligns more effectively with the causality nature of the UBTP task.
Table 6: Model performance MoviesLens- 1M (target length=5).
Backbone SHR@5
SNDCG@S1
SHR@101 t
SNDCG@ 10
SMatch@50 f
SMatch 100 t PPL 1
Bidirectional
0.1159
0.0662
0.1925
0.0806
0.1500
0.2709
31.35
Prefix
0.1175
0.6517
0.1927
0.7966
0.1521
0.2740
30.86
Causal
0.1218
0.0679
0.1983
0.0825
0.1559
0.2796
30.36

---

PifferDiff
DiffuRee
LPDO
Mean:-0.035
Mean:
0.067
Std: 2.045
Std: 1.740
Std: 1.375
DCRec
DreamRec
Information Abundance (1A)
30
25
20
10
Mean: 0.033
Meam:-0.000%
Std: 1.718
Std: 0.0840
LeDo
octer
SAster
pinutte
Protertirt
Drainfec
Figure 6: Information Abundance (IA) of model embeddings and T-SNE results of ML-1M (len=5).
Embedding Analysis
In Figure we illustrate the Information Abundance (IA) 46 results of embeddings generated by six models and provide detailed visualization of the embedding layers for five diffusion-based models. LPDO achieves the highest IA score and exhibits more diverse embeddings. highlighting the effectiveness of our proposed approach. On the other hand. PreferDiff and DreamRee suffer from embedding collapse, likely due to optimization without incorporating ranking loss.
K Overall Performance Comparison
this section, we provide all evaluation results on Amazon Beauty (len=3), MovieLens (len=5/10) and LastFM (len=S/10) as shown in Table 7
Table
S
Table
Table 10 and Table II respectively.
Table 7: Overall Performance Comparison on Amazon Beauty (len=3).
Metric
FPMC
SASRec
SASRec-ar
STOSA
DiffuRec
DreamRe:
PreferDiff
DCRcc
Improve.
M5
0.0251
0.0226
0.0215
0,0251
0.0303
0.0002
0.0028
0.0260
0.0344
13.53%
MeamHR@11
0.0390
0.0470
0.0458
0.0410
0.0471
0.0007
0.0057
0.0487
0.0549
16.56%
MeunllR@00
0.0622
0.0690
0.0688
0.0583
0.0847
0.0016
0.0096
0.0742
0.1008
99.01%
MeanNDCG@s
0.0138
0.01
0.0118
0.0125
0.0150
0.0001
0.0011
0.0141
0.0184
22.67%
MeanNDCG@11 10
0.0162
0.0201
0.0196
0.0172
0.0192
0.0003
0.0028
0.0169
0.0224
11.44%
McaNNDCG@20
0.0193
0.0213
0.0211
0.0183
0.0271
0.0006
0.0031
0.0229
0.0326
20. 30%
Sc
0.0236
0.0219
0.0218
0.0238
0.0274
0.00002
0.0025
0.0250
0.0307
12.04%
SegHR 10
0.0376
0.0466
0.0455
0.0407
0.0442
0.0006
0.0055
0.0388
0.0503
7.94%
ScgHR@20
0.0619
0.0690
0.0667
0.0581
0.0842
0.0014
0.0093
0.0729
0.0982
16.63%
SegNDCG@5
0.0129
0.0114
0.0114
0.0120
0.0149
0.0001
0.0015
0.0135
0.0164
10.07%
SegNDCG@10
0.0158
0.0188
0.0003
24.62%
SegNDCG@20
0.0193
0.0212
0.0210
0.0182
0.0270
0.0005
0.0030
0.0225
0.0322
19.26% 26%
SegMatchi
0.0253
0.0257
0.0363
e 100
0.0598
0.0437
0.0446
0.0318
0.0852
0.0000
0.0004
0.0807
0.0940
10.33%
P
37.56
51.25
89.55
38.90
25

---

Table 8: Overall Performance Comparison on LastFM (len=5).
Metric
FPMC
SASRec
SASRec-ar
STOSA
DiffuRoc
DreamRee
PreferDiff
DCRec
LPDO
Improve.
McanHR@5
0.1637
0.1819
0.1831
0.1548
0.1797
0.0435
0,0037
0.1977
0.2553
29.14%
MeanHR 6 10
0,2312
0,2528
0.2560
0,2189
0.2462
0.0536
0,0069
0.7755
0.3295
20.48%
MeanHR
0.3313
0.3437
0.3463
0,3019
0.3293
0.0789
0.0144
0.3425
0.4154
19.95%
McanNDGG@5
0,0830
0.0918
0.0909
0,0765
0.0909
0.0206
0,0024
0.0992
0.1277
28.73%
MeanNDCG@10 10
0.0898
0.0954
0.0975
0.0838
0.0922
0.0188
0.0031
0.1033
0.1210
24.10%
McanNDCG@20
0,0997
0,1021
0.1016
0,0897
0.0940
0.0209
0,0046
0.1142
0.1340
17.34%
S
0.1636
0.1816
0.1829
0.1537
0.1793
0.0433
0.0035
0.31
0.2507
29.83%
SegHR 10
0.2311
0.2523
0.2564
0.2184
0.2458
0.0531
0,0065
0.2681
0.3244
26.52%
Se
0.3310
0.3436
0.3461
0.3016
0.3288
0.0738
0.0140
0.3380
0.4123
19.13%
SegNDCG@s
0.0830
0.0917
0.0908
0,0760
0.0906
0.0205
0,0023
0.0972
0.1260
29.63%
SegNDCG@ 10
0.0897
0,0953
0.0972
0.0836
0.0921
0.0185
0.0028
0.1015
0.1195
17.73%
ScgNDCG@20
0.0996
0.1020
0.1016
0,0896
0.0938
0.0209
0.0043
0.1132
0.1235
9.10%
SegMatch 50
0.1636
0.1578
0.1633
0,14
0.1638
0.0189
0.0000
0.1725
0.2357
36.81%
SegMatch 100
0,2833
0.2289
0.2395
0.2216
0.2578
0.0209
0.0010
0.2314
0.3268
26.76%
PPL.
39.29
28.26
28.20
30.65
30,5495
149,9894
> 500.0
29.28
27.28
3.26%
Table 9: Overall Performance Comparison on LastEM (len=10).
Metric
FPMC
SASRec
SASRec-ar
STOSA
DiffuRec
DreamRe:
PreferDiff
DCRec
LPDO
Improve.
MeanHI
0.1093
0.1170
0.1151
0.0894
0.1222
0.0297
0.0035
0.1401
0.1805
28.84%
MeanHR @ 10
0.1717
0.1611
0.1658
0.1499
0.1734
0,0413
0.0086
0,2099
0.2470
17.68%
@c 20
0,2680
0.2353
0.2347
0.2153
0.2468
0.0623
0.0212
0.2601
0.3200
23.03%
McanNDCG@5
0.0608
0,0615
0.0598
0,0475
0.0635
0.0144
0.0022
0.072
0.0931
29%
McunNDG@@10
0,0694
0.0613
0.0647
0.0630
0.0674
0.0159
0.0041
0.0773
0.0925
19.66%
McanDDGG@20
0,0838
0,0707
0.0693
0.0657
0.0740
0.0194
0,0096
0.0735
0.0899
7.28%
SeqHR
0.1080
0.1163
0.1148
0.0888
0.1209
0.0290
0.0000
0.1311
0.1705
30.05%
SeyHRG 10
0,1703
0,1606
0.1654
0,1495
0.1715
0.0407
0,0074
0.1881
0.2362
25.57%
SeqHR 20
0.2670
0.2348
0.2341
0.2147
0.2450
0.0606
0.0197
0.2481
0.3113
25.47%
SegNDCG@5
0.0598
0,0608
0.0597
0,0471
0.0625
0.0141
0,0000
0.0673
0.0879
30.61%
SegNDCG@ 10
0.0686
0.0610
0.0645
0.0624
0.0665
0.0159
0.0033
0.0730
0,0889
21.78%
SegNDCG@20 20
0.0835
0.0705
0.0690
0.0652
0.0734
0.0187
0.0086
0.0706
0,0850
24.65%
SegMatch@ 50
0,0713
0.0635
0.0566
0.0449
0.0586
0.0098
0.0000
0.0557
0.0762
6.87%
S 100
0.1067
0.1106
0.0957
0.0850
0.1045
0.0107
0.0000
0.0771
0.1162
3.06%
PPL I
83.16
61.69
61.56
66.41
65.29
283.50
> 500.0
61.32
60.93
0.64%
Table 10: Overall Performance Comparison on ML- IM (len=5).
Metric
FPMC
SASRec
SASRec-ar
STOSA
DiffuRec
DreamRec
PerferDiff
DCRcc
LPDO
Improve.
MeanHR @5
0.0158
0.0807
0.0798
0.0865
0.0809
0.0029
0.0094
0.1129
0.1241
9.92%
MeanHR @ 10
0,0372
0.1372
0.1373
0.1478
0.1548
0.0055
0.0165
0.88
0.2017
6.89%
MeanHR 20
0.0802
0.2238
0.2249
0.2375
0.2490
0.0099
0.0297
0.889
0.3100
6.93%
McanNDCG@5
0.0100
0,0455
0.0447
0.0494
0.0510
0.0017
0.0049
0.0632
0.0692
9.49%
MeanNDCG@10
0.0181
0.0577
0.0578
0.0629
0.0653
0.0024
0.0073
0.0772
0.0838
8.55%
McanNDCG@20
0.0290
0.0713
0.0722
0.0758
0.0797
0.0034
0.0104
0.0909
0.0963
5.94%
SegHR
0.0157
0.0895
0.0795
0.0865
0.0894
0.0028
0.0004
0.1
0.1218
10.03%
1
0.0371
0.1365
0.1366
0.1476
0.1540
0.0054
0.0165
0.23
0.1983
8.78%
0.0802
0.2222
0.2232
0,2370
0.2476
0.0098
0.0296
0.2853
0.3051
6.94%
SeyNDCG@s
0.0098
0.0434
0.0445
0.0493
0.0506
0.0016
0.0049
0.0621
0.0679
9.34%
SegNDCG@ 10
0.0179
0.0573
0.0574
0.0627
0.0649
0.0023
0.0073
0.0759
0.0825
8. 8.70%
Sc
0.0290
0.0708
0.0716
0,0757
0.0792
0.0034
0.0104
0.0897
0,0949
5.80%
SegMatch 50
0.0160
0.1045
0.1049
0.1074
0.1
0.0000
0.0000
0.1458
0.1559
6.92%
SegMatch@ 100
0.0597
0.2099
0.2017
0,2086
0.2271
0.0000
0.0002
0 0686
0.2796
4.17%
PPL.
38.43
33.62
33.58
33.47
32.47
165.59
> 500.0
31.42
30.36
3.37%
Table 11: Overall Performance Comparison on ML- IM (len=10).
Metric
FPMC
SASRec
SASRec-ar
STOSA
DiffuRec
DreamRec
PreferDinf
DCRsc
LPDO
Improve.
55
0.0060
0.0584
0.0565
0.0477
0.0632
0.0023
0.0080
0.0752
0.0861
13.74%
MeanHR @ 10
0.0144
0,1443
0.0996
0.0868
0.1091
0.0043
0.0104
0.1340
0.1482
10.60%
McanHR@2 @
0.0368
0.1723
0.1686
0.1473
0.1808
0.0081
0.0208
0.2253
0.2398
6.43%
McanNDCG@s
0,0038
0.0333
0.0323
0.0276
0.0361
0.0013
0.0045
0.0434
0.0486
11.98%
McanNDCG@10
0.0070
0.0451
0.0431
0.0379
0.0464
0.0019
0.0107
0.0575
0.0628
9.22%
McanNDCG@20
0,0141
0.0556
0.0551
0.0483
0.0586
0.0027
0.0101
0.0731
0.0766
4.79%
SeglIR@5
0.0058
0.0581
0.0560
0.0476
0.0624
0.0022
0.0077
0.0717
0.0819
14.22%
0,0140
0,1033
0.0985
0.0864
0,1075
0.0043
0.0101
0.1277
0.1419
11.1
Se 20
0.0361
0.1706
0.1670
0.1467
0.1782
0.0080
0.0206
0.2170
0.2306
6.27%
SeyNDCG@5
0.0036
0.0331
0.0320
0.0276
0.0356
0.0012
0.0043
0.0412
0.0461
11.89%
SeuNDCG@ 10
0.0068
0.0446
0.0426
0.0377
0.0456
0.0018
0.0006
0.0550
0.0603
9.63%
SeyNDCG@20
0.0139
0.0551
0.0546
0,0480
0.0578
0.0027
0.0101
0.6707
0.0738
4.38%
SegMatch 50
0.0000
0.0299
0.0261
0.02
0.0311
0.0000
0.0000
0.0381
0.0447
17 32%
SegMatch 100
0.0032
0.0801
0.0770
0.0614
0.0856
0.0000
0.0000
0.0977
0.1084
10.07%
PPL.
85,55
68.99
70.41
73.92
68.35
305.19
> 500.0
68.58
67.44
1.66%
26


Reviews:
[{"review_id": "qpnNoJJUip", "reviewer": "Reviewer_WfsB", "summary": "* This paper considers recommender systems and has three contributions:\n    * It proposes a new problem, User Behavior Trajectory Prediction (UBTP), of predicting a sequence of a user's preferred items in the future k time steps by using this user's history of viewed items in the past n time steps.\n    * It adopts a diffusion model to do such prediction, proposing a method called Listwise Preference Diffusion Optimization (LPDO). The diffusion model's output is k embeddings, and each embedding is a vector of utilities for all the items. For each of the k future time steps, the system predicts the user's top-K items according to the output of the diffusion model.\n    * It proposes a new metric to evaluate the performance of UBTP, by checking how often the top-K predicted items actually contain the true most-preferred items.\n* This paper evaluated LPDO using 4 real-world datasets, where k is set to 3, 5, or 10, against 7 baselines. It shows that LPDO outperformed significantly all of them.", "questions": "* Line 53-59 tries to explain why the proposed method LPDO outperforms previous methods, but are too technical to fully grasp in the introduction section. Fig.1 clearly explains the insight of why Fig.1(c) is beneficial, but is not echoed by the technical presentation of LPDO. It could be helpful in the later section of the paper to explain why LPDO's new loss function can achieve Fig.1(c), improving upon previous work in Fig.1(b).\n* Line 153 mentioned that the paper follows [18] to also include history H as part of X0, which the model is trying to generate. I am wondering why this is helpful. Could you provide some insights to explain this design consideration?\n* Line 157 says that pθ(X_{t−1} | Xt, H). I thought that for each t, the history H is already a part of Xt. So why do we have the extra \"H\" in `pθ(X_{t−1} | Xt, H)`?\n* Eq.11 introduces the loss for listwise preference. However, it seems that `L_ListPref` is defined for a particular future time step j? How would the system combine all the k future time steps in the loss, considering that the system is trying to capture the causal relation between those k future time steps?\n* Eq.16 contains both reconstruction loss and list preference loss. I thought the reconstruction loss already contains the list preference loss, as the reconstruction loss is about the loss of the reconstructed k future step predictions?", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "* Strength\n    * The proposed problem is well-motivated.\n    * The proposed metric aligns well with the proposed problem.\n    * The proposed algorithm empirically significantly outperformed baselines.\n* Weakness\n    * One concern is that the key innovation and insights behind the proposed method, LPDO, are a bit unclear, making it hard to fully appreciate its technical novelty. For more details, please refer to the \"Questions\" section later in the review.\n    * Another concern is that the empirical analysis is a bit unclear about the key contributor to the improved performance of the proposed method. I think there could be a couple of factors why the proposed method outperformed previous methods: (1) it tries to predict k future time steps, rather than 1 time step; (2) its novel loss function; (3) it uses the causal transformer. It could be helpful to better understand the contribution of these factors. A better understanding of this question could allow the readers to appreciate the technical novelty more.\n        * Also, related to factor (1), since the proposed method predicts a longer future, would it require more data or a longer time to train? Understanding this question could allow potential users to better decide when to use the proposed method.\n* Minor\n    * Line 119: \"target item\" is confusing, as it makes me confused whether this refers to the single-item prediction task or the proposed UBTP task, which tries to predict k items.\n    * Line 158: `Equation (24)` is mistakenly referred I think.\n    * Line 190: `Section 3` is mistakenly referred I think.", "was_revised": true, "final_justification": "This paper proposes to use a diffusion model to predict future users' preferred items. The rebuttal clarified my questions. I think it contributes a new tool to user trajectory prediction. I will keep my rating.", "rebuttal": "We are truly grateful for the time and effort you dedicated to reviewing our work. We hope our detailed responses have clarified the issues raised.\n\n> W1&Q1: The key innovation and insights are a bit unclear. Lines 53–59 are too technical for the introduction. Fig.1(c) is not echoed by the technical presentation.\n\nThank you for your thoughtful feedback and suggestions. The key advantage of our proposed LPDO method is that it directly optimizes the listwise preference of item sequences as shown in Fig.1(d), rather than optimizing individual items independently as in pointwise methods. This listwise optimization allows LPDO to better capture the dependencies and overall ranking quality of the entire sequence, leading to improved recommendation performance. Figure 1(c) is meant to conceptually illustrate how our preference-aware diffusion model focuses the prediction distribution more effectively on semantically related targets. We elaborate this effect formally in Section 4.2 (Bridging Diffusion and Sequential Listwise Ranking) and Section 4.4 (Connecting Diffusion Models With Listwise Maximum Likelihood Estimation), where we introduce the ListPref loss and the ELBO formulation. By aligning the diffusion denoising steps with the Plackett–Luce listwise supervision signal, the model is guided to concentrate generation probability on ranked, preference-consistent item sequences, thereby reducing the dispersion toward unrelated content. We will clarify this in revised version. \n\n---\n\n> W2:  The empirical analysis is a bit unclear about the key contributor to the improved performance of the proposed method. There could be a couple of factors why the proposed method outperformed previous methods: (1) k-step prediction; (2) novel loss function; (3) causal transformer.\n\nThank you for raising this point. As you mentioned, the performance improvement of LPDO mainly comes from three factors:\n\n- **Designed for k-step prediction**: LPDO is specifically designed for the k-step prediction task. While all baselines are extended to support prediction over k future time steps for fair comparison, LPDO is the first model explicitly designed for the UBTP task, addressing the limitations of directly applying next-item prediction models in this setting.\n\n- **The novel loss function**: We proposed a novel listwise preference-aware loss. Our loss maximizes the\njoint likelihood of the entire ordered sequence, better capturing the ordering and dependencies among items. We have provided an ablation study of different loss components in LPDO in Tab.2. The results demonstrate the effectiveness of our loss. \nFurthermore, we replace the original list preference loss in LPDO with traditional cross-entropy loss for directly comparison. The results on ML-1M (target length=5) presented below indicate the importance of list-wise optimization in the UBTP task.\n\n|Loss type|SHR@5 ↑|SNDCG@5 ↑|SHR@10 ↑|SNDCG@10 ↑|SMatch@50 ↑|SMatch@100 ↑|PPL ↓ |\n|-|-|-|-|-|-|-|-|\n|Cross Entropy|0.1103|0.0645|0.1914|0.0801|0.1477| 0.2659|31.35|\n|ListPref|0.1218|0.0679|0.1983|0.0825|0.1559|0.2796|30.36 |\n\n- **Applying causal transformer**: Regarding transformer modules, we provide a comparison between different transformer modules, including bidirectional [1], prefix [2], causal [3], on ML-1M (target length=5) as below. The results show that causal transformer outperforms the other two types, which indicates the importance of capturing performance and causality among user iterations.\n\n| Transformer|SHR@5 ↑|SNDCG@5 ↑|SHR@10 ↑|SNDCG@10 ↑|SMatch@50 ↑|SMatch@100 ↑|PPL ↓ |\n|-|--|-|-|-|-|-|-|\n|Bidirection|0.1159|0.0662|0.1925|0.0806|0.1500|0.2709|31.35|\n|Prefix|0.1175|0.6517|0.1927|0.7966|0.1521|0.2740|30.86|\n|Causal|0.1218|0.0679|0.1983|0.0825|0.1559|0.2796|30.36|\n\n---\n\n> W3:  Since the proposed method predicts a longer future, would it require more data or a longer time to train?\n\nThank you for bringing up this point. It is worth noting that both LPDO and other baselines demand more training data to reach optimal performance. This is largely because the UBTP task entails a significantly larger solution space than next-item prediction, expanding from $n$ to $n^k$, where $n$ is the number of candidate items and $k$ is the number of steps to predict. \n\nTo further investigate this issue, we analyze model performance (measured by SeqMatch@50) on the ML-1M dataset (target length = 5) under varying training set sizes: the full dataset, 3,000 samples, and 1,000 samples. As shown below, model performance improves consistently with more training data. Notably, LPDO consistently outperforms all baselines across all three data settings.\n\n| Num of data | SASRec | DiffuRec | DCRec  | LPDO   |\n|-------------|--------|----------|--------|--------|\n| All         | 0.1045 | 0.1168   | 0.1458 | 0.1559 |\n| 3000        | 0.0973 | 0.1097   | 0.1280 | 0.1334 |\n| 1000        | 0.0548 | 0.0599   | 0.0671 | 0.0849 |\n\nRegarding training time, as shown in Fig. 3(a), our model converges faster than the baseline due to LPDO`s optimization for global sequence-level preference.\nThus, LPDO does not increase the training cost compared to other baselines; rather, it enhances both computational efficiency and predictive effectiveness.\n\n\n---\n\n> W4: Line 119: \"target item\" is confusing.\n\nThank you for your insightful feedback. The subsection around Line 119 is intended to introduce diffusion models and their general application in recommender systems. The specific application of diffusion to the UBTP task, which involves predicting a sequence of k items, is detailed in Section 4.1. We will revise the manuscript to clarify this distinction and avoid potential confusion.\n\n---\n\n> W5&W6: Line 158 and Line 198 is mistakenly referred.\n\nThank you for pointing out the incorrect references. We will carefully review and correct these references in the revised version.\n\n---\n\n> Q2: Line 153 mentioned that the paper follows [18] to also include history H as part of X0, which the model is trying to generate.\n\nThank you for this insightful question about our design choice! The concatenation of history H and target z is first proposed by DiffuSeq [4] in the NLP task, and then DCRec [5] introduce it in the sequential recommendation task for conditioning diffusion models. This can better capture detailed sequential patterns and contextual information from the user’s history [5]. Based on this, we introduce causal attention to further capture the preference evolution. As shown in Fig.2, the reverse/generation process starts from $X_T$, where $H_T$ and $z_T$ are noised. $H_t$ in each diffusion steps can provide extra historical user information during the generation until obtaining clean $H_0$ and $Z_0$. \n\nEmpirically, we observe that this concatenation-based conditioning significantly improves the guidance signal during generation compared to approaches that do not explicitly model the historical context in this manner (e.g., DreamRec [6], PreferDiff [7]). As a result, our method achieves more accurate and user-preferred recommendations. \n    \n---\n\n> Q3: For each $t$, the history $H$ is already a part of $X_t$. Why do we have the extra $H$ in $p_\\theta(X_{t-1}| X_t, H)$?\n\nThank you for the insightful comment. We would like to clarify that, in addition to the $H$ component within $X_t$, there is an extra $H$ used as direct conditioning, as illustrated in Fig.2. This additional conditioning serves as the input to the cross-attention layer and plays a crucial role in guiding the generation process. This strategy was first introduced in Stable Diffusion [8] and later adopted in DCRec [5] for recommendation tasks. We thank the reviewer for this insightful question and will enhance the explanation accordingly in the revised manuscript.\n\n---\n\n> Q4: It seems that $L_{ListPref}$ is defined for a particular future time step j? How would the system combine all the k future time steps in the loss?\n\nThank you for highlighting the potential ambiguity in our presentation of the listwise loss. \nEquation (11) was framed as “per‐step” $L_{\\rm ListPref}(j)$ simply to keep the expression compact and to focus the reader’s attention on the mechanics of the listwise term at a single horizon $j$. In fact, the full listwise objective used in all our experiments is the sum of these per‐step losses over $j=1,\\ldots,k$, exactly as shown (and implemented) in the model code and in Equation (16). By summing across all $k$ positions and employing our cross‑step attention blocks inside the Cross‑Conditional Diffusion Transformer, the model naturally receives joint gradient signals that enforce causal consistency between early and later predictions. In this way, the loss truly operates on the entire future sequence, not just on each step in isolation.\n\n---\n\n> Q5: Eq.16 contains both reconstruction loss and list preference loss. I thought the reconstruction loss already contains the list preference loss.\n\nThank you for raising this point. We would like to clarify that Eq.(16) is derived from Eq.(5), with the primary modification being the introduction of the list preference loss, a novel ranking objective specifically designed for the UBTP task, replacing the original ranking loss in Eq.(5). Meanwhile, the reconstruction loss and regularization loss are preserved. We appreciate this constructive feedback and will revise the manuscript accordingly to enhance clarity.\n\n[1] BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding\n\n[2] Exploring the limits of transfer learning with a unified text-to-text transformer\n\n[3] Language Models are Unsupervised Multitask Learners\n\n[4] Diffuseq: Sequence to sequence text generation with diffusion models\n\n[5] Dual conditional diffusion models for sequential recommendation \n\n[6] Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion\n\n[7] Preference Diffusion for Recommendation\n\n[8] High-Resolution Image Synthesis with Latent Diffusion Models"}, {"review_id": "oYHu16B65N", "reviewer": "Reviewer_ULMe", "summary": "This work tackles the complex problem of forecasting user behaviour trajectories multiple steps into the future, a problem distinct from regular sequential recommendation. Generative recommendation with diffusion models is becoming more and more prevalent across the recommender systems research community due to the ability of such models to model uncertainty and learn latent data distributions in order to produce diverse recommendations. However, diffusion models are typically currently limited to next-item recommendation settings due to their inability to account for the dynamic nature of user preferences across stages of a predicted user behaviour trajectory. Point-wise preference signals can be incorporated, but joint dependences and relative ordering of items is still ignored, two factors which considerably impact the quality and impact of a sequence of recommendations. This work aims to address these issues directly.\n\nThe first contribution provided by this work is the formalisation of this task (UBTP) of forecasting an ordered sequence of $k$ interactions. In this problem setting, the authors propose a novel approach termed LDPO which integrates Plackett-Luce ranking terms into the evidence lower bound (ELBO) of a non-autoregressive diffusion model in continuous latent space. Deriving this tractable lower bound which jointly handles reconstruction and listwise likelihoods, whilst simultaneously ensuring stable training and managing the generation fidelity-preference alignment trade-off is a non-trivial task, which the authors tackle through devising an end-to-end differentiable scoring head mapping denoised latents to logits and formulating a tight decomposition of the ELBO. Additionally, the authors also introduce a new metric, SeqMatch, which is specifically designed for evaluating multi-step recommendation quality. Specifically, SeqMatch@$k$, computes the percentage of test user trajectories where each item in the trajectory is present in the model’s top $k$ predictions for their respective positions.\n\nExperimental results are provided exploring the performance of LPDO compared to competing baselines and to other diffusion-based methods, with some additional studies performed on the impact of different hyperparameters on performance. Several large-scale, widely used recommendation benchmark datasets are used for evaluation, and a range of both traditional and generative recommendation algorithms are evaluated alongside LPDO. The authors find that their approach outperforms the selected baselines across the board and that LPDO converges faster than other diffusion-based methods.", "questions": "**Q1** - As mentioned above, I have very little to ask as the paper is very thorough, and I recommend acceptance. One question I do have is whether the authors could expand further on the rationale behind not providing open-source access to the code for the implementation? The high potential for impact that this paper has could be limited somewhat by not providing a base implementation for further research to easily progress onwards from.\n\n**Q2** - The authors note in the checklist that the improvements in performance are statistically significant, but this is not included in the main text. Could you confirm that this is the case for all experiments conducted, and if not, could these cases be flagged in the results table (e.g. via an asterisk or simply un-bolding the result)?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n* Overall, the work is novel and well-motivated. Diffusion models may be gaining prevalence for large-scale recommendation, however tackling this problem of multi-step trajectory forecasting in a manner which properly accounts for the ordering and causal relationships between items in a given trajectory is a key step in ensuring these methods are more widely applicable in real-world scenarios. This work clearly appears to be a considerable step towards addressing this problem, and as such has potential for significant impact.\n* The paper itself is very well structured and clear throughout; aspects of the model formulation, derivation of the variational lower bound and the training procedure are all outlined concisely and clearly, and on inspection all the work appears sound and of high quality. Likewise, the evaluation of the model and the competing methods is presented in an easily parsed and engaging manner, with the key takeaways being clearly signposted and explained in depth.\n* The empirical results are very good, with the proposed technique in some cases providing very significant improvements over the competing baselines, across all of the datasets used for testing. The evaluation has been thoroughly carried out, with a range of different metrics used to show the superior performance of the proposed method.\n* A particular strength of this work is the choice by the authors to formulate not only the task being studied, but also a more relevant metric for evaluation. Often, having a clear target, problem statement and metric for improvement is the most important factor in driving forward progress in a certain area of research, and I think contributions such as this which attempt to provide these things can be highly impactful in the sense that they incentivise future work on the topic, driving further developments.\n\n**Weaknesses**\n* Ultimately, I have very few negative things to say about the paper. It’s very well constructed and presented, is novel, addresses a clear problem, and evidences the claims included with thorough evaluation. \n* One clear weakness is the lack of open-source code, as this will limit the impact of the paper given that it is more challenging for practitioners to use the technique, and more time consuming for researchers to pursue further work based on this approach. I appreciate that this may not be possible for certain reasons, however it does certainly limit the impact.\n* As mentioned in the questions section below, some further clarity about which of the experimental results are statistically significant would be appreciated, as this is not immediately clear from the results tables.", "was_revised": true, "final_justification": "The authors have addressed my concerns regarding code availability and statistical significance during the rebuttal phase, but my overall assessment of the paper remains unchanged from my original score.", "rebuttal": "We sincerely thank the reviewer for the detailed, thoughtful, and positive evaluation of our work. We are especially grateful for your recognition of our contributions. Your comments on the clarity of presentation, strength of empirical results, and potential impact are highly encouraging and greatly appreciated.\n\n> W2, Q1: The lack of open-source code.\n\nThank you for raising this point. We plan to release the data and code after the paper is published.\n\n---\n\n> W3, Q2:  Some further clarity about which of the experimental results are statistically significant would be appreciated.\n\nThank you for the suggestion. We confirm that the improvements are statistically significant for the main performance results (Sec. 5.1), factor analysis (Sec. 5.2), and ablation study (Sec. 5.3). We will clarify this in the revised manuscript and ensure that statistical significance is reported for all other experiments (in appendix)."}, {"review_id": "LfSpqDTe5d", "reviewer": "Reviewer_EHty", "summary": "This article proposes a novel diffusion based framework LPDO (List Preference Diffusion Optimization) for user behavior trajectory prediction, which uses a generative paradigm to predict users' future interaction trajectories. The author believes that existing diffusion based recommendation models largely handle each position independently, thereby ignoring global list dependencies. The LPDO proposed in this article addresses this limitation by directly incorporating Plackett Luce list based ranking targets into diffusion ELBO, thereby aligning the generation process with trajectory level preferences. It also introduced a new metric, SeqMatch, for rigorous trajectory level evaluation and conducted extensive experiments, achieving the most significant results compared to strong baselines on four datasets.", "questions": "Please refer to Weaknesses section.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths：\n1. The ELBO formulation incorporating Plackett-Luce likelihood provides a principled bridge between generative denoising and listwise ranking. The derivation of the tight variational bound is a notable theoretical contribution.\n2. The List Preference Diffusion Optimization (LPDO) framework proposed in this article is innovative in integrating list preference information into diffusion models. This method aligns the backpropagation process with the list ranking target, which is a new approach to improve the consistency and accuracy of predicting user behavior trajectories.\n3. LPDO achieves ​faster convergence and enables ​single-step inference​, reducing inference latency.\n\nWeaknesses:\n1. From Figure 3 (b), it is shown that the prediction results for long-term goals are similar to those for short-term goals, and LPDO shows a similar decrease in this prediction result compared to other sequence recommendation methods (pos1-pos5). This does not seem to reflect the superiority of LPDO in modeling users' long-term preferences compared to other methods.\n2. The expression in the paper is not clear enough, such as the \"UBTM\" in line 149, which is not explained in the entire text.\n3. The experimental results of various models at different prediction lengths are shown in Table 1. LPDO did not show a significant increase in advantages compared to other models at longer lengths (len=10) and shorter lengths (len=5)\n4. ​Hyperparameter Sensitivity: Performance heavily depends on manual tuning of loss weight λ and penalty γ. Optimal γ varies across datasets (0.0–0.8), raising generalizability questions. An adaptive tuning strategy or ablation on sensitivity is missing.\n5. The model requires ​fixed-length trajectories during training​. Real-world sequences are variable-length, limiting applicability to open-ended scenarios.\n2. Why is it that setting the diffusion step size to 50 and the sampling step size to 1 can yield very significant results?", "was_revised": false, "final_justification": "", "rebuttal": "We greatly appreciate your time and effort in reviewing our work. Your comments were very helpful, and we have provided detailed responses below to clarify and address the issues you raised.\n\n> W1: From Figure 3 (b), it is shown that the prediction results for long-term goals are similar to those for short-term goals, and LPDO shows a similar decrease in this prediction result compared to other sequence recommendation methods (pos1-pos5). This does not seem to reflect the superiority of LPDO in modeling users' long-term preferences compared to other methods.\n\nThank you for the insightful comments. We try to address these concerns from two distinct perspectives:\n\n- **Performance decay is inherent in the UBTP task.**  Compared to one-step prediction, UBTP is intrinsically more challenging due to error accumulation over multiple steps. As the model predicts further into the future, uncertainty compounds, and performance naturally declines due to error propagation. This is a well-known phenomenon in multi-step sequence modeling, such as the NLP task [1]. Despite this, LPDO demonstrates greater robustness and slower degradation than other methods, underscoring its effectiveness.\n\n- **A similar performance trend does not equate to having similar modeling capabilities.** While it is true that all models, including LPDO, demonstrate a decreasing accuracy trend across future positions, this observation alone does not imply comparable modeling capacity. As illustrated in Fig.3(b), LPDO consistently outperforms all baselines at each prediction step, including the later stages. This consistent advantage highlights LPDO’s superior ability to capture both short-term signals and long-term user preferences.\n\nWe thank the reviewer for the insightful comment and acknowledge that there is still potential for enhancing the UBTP task in future work.\n\n---\n\n> W2: The expression in the paper is not clear enough, such as the \"UBTM\" in line 149.\n\nThank you for pointing this out. ‘UBTM’ is a typo and should be ‘UBTP’. We will revise the manuscript to correct this.\n\n---\n\n> W3: LPDO did not show a significant increase in advantages compared to other models at longer lengths (len=10) and shorter lengths (len=5).\n\nThank you for bringing this point to us. We would like to clarify that LPDO consistently demonstrates substantial performance improvements across both shorter (len=5) and longer (len=10) future sequence prediction as shown in Tab.1.\n\nFor instance, on the Last-FM (target len=5) setting, LPDO achieves a 29.83% improvement over the best baseline in SeqHR@5, and a 36.81% absolute gain in SeqMatch@50, which measures strict trajectory-level accuracy. On the LastFM (target len=10) dataset, LPDO improves SeqHR@5 by 30.05% and SeqMatch@50 by 6.87\\% over the best baseline. These gains remain substantial and statistically significant, and they underscore LPDO’s robustness across different settings.\n\n---\n\n> W4: Performance heavily depends on manual tuning of loss weight $\\lambda$ and penalty $\\gamma$.\n\nThank you for bringing this point to us. We would like to clarify that loss weight $\\lambda$ can be set to 0.1 for all experiment settings to achieve superior performance, as mentioned in Sec.5.1. As for the penalty factor $\\gamma$, as shown in Fig.3(c) and the additional results below, all different $\\gamma$ settings consistently outperform the baselines in Tab.1, demonstrating the robustness of our method to this hyperparameter.\n\n**Table: MovieLens-1M (len=5)**\n| Metric      | SASRec | DiffuRec | DCRec  | LPDO($\\gamma$=0.0) | LPDO($\\gamma$=0.3) | LPDO($\\gamma$=0.5) | LPDO(γ=0.8) |\n|-------------|--------|----------|--------|-------------|-------------|-------------|-------------|\n| SHR@5       | 0.0895 | 0.0894   | 0.1107 | 0.1190      | 0.1218      | 0.1184      | 0.1164      |\n| SNDCG@5     | 0.0434 | 0.0506   | 0.0621 | 0.0637      | 0.0679      | 0.0651      | 0.0641      |\n| SMatch@50   | 0.1045 | 0.1074   | 0.1458 | 0.1509      | 0.1559      | 0.1558      | 0.1523      |\n\n**Table: LastFM (len=5)**\n| Metric      | SASRec | DiffuRec | DCRec  | LPDO($\\gamma$=0.0) | LPDO($\\gamma$=0.3) | LPDO($\\gamma$=0.5) | LPDO($\\gamma$=0.8) |\n|-------------|--------|----------|--------|-------------|-------------|-------------|-------------|\n| SHR@5       | 0.1816 | 0.1793   | 0.1931 | 0.2367      | 0.2388      | 0.2403      | 0.2507      |\n| SNDCG@5     | 0.0917 | 0.0906   | 0.0972 | 0.1150      | 0.1213      | 0.1211      | 0.1260      |\n| SMatch@50   | 0.1578 | 0.1638   | 0.1723 | 0.2205      | 0.2292      | 0.2300      | 0.2357      |\n\n\nWe will add additional results in the revised version to improve the clarity of $\\gamma$ settings. Thank you for your suggestion regarding adaptive tuning. We will consider incorporating adaptive strategies in future work.\n\n---\n\n> W5: The model requires fixed-length trajectories during training. Real-world sequences are variable-length, limiting applicability to open-ended scenarios.\n\nThank you for raising this concern. We would like to clarify that our model can support variable-length sequences during training. Our model is designed for the UBTP task (next-sequence prediction), which is an extension of the next-item prediction setting in sequential recommendation. In this field, it is standard practice to use sequences with a maximum length for training, and variable-length sequences are typically handled by padding shorter sequences to the maximum length, which is a widely adopted and effective strategy in sequence modeling. Therefore, our method can naturally support variable-length trajectories without loss of generality or applicability. During model inference, our model can also support variable-length sequences. \n\nThus, our method remains applicable to open-ended scenarios and real-world deployment. We will clarify this implementation detail in the revised version.\n\n---\n\n> W6: Why is it that setting the diffusion step size to 50 and the sampling step size to 1 can yield very significant results?\n\nThank you for your question. Compared to CV [2] and NLP [3] tasks, recommendation targets lie in a low-dimensional, discrete, and highly structured space (e.g., item indices). The conditional signals, such as user history, are strong and tightly constrain the output manifold. As a result, even coarse denoising with a single sampling step can reliably recover high-quality item representations for ranking. In contrast to NLP/CV tasks requiring fine-grained generation, the discrete and sparse nature of recommender outputs makes them significantly more robust to approximation during fast sampling. Meanwhile, our observation is consistent with prior works such as DiffRec[4], SdifRec[5], and DCRec[6], which also report that a small number of steps can yield competitive results in recommendation tasks. We will clarify this point in the revised version.\n\n[1] Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks\n\n[2] High-Resolution Image Synthesis with Latent Diffusion Models\n\n[3] DiffuSeq: Sequence to Sequence Text Generation with Diffusion Models\n\n[4] Diffusion Recommender Model\n\n[5] Bridging User Dynamics: Transforming Sequential Recommendations with Schrödinger Bridge and Diffusion Models\n\n[6] Dual Conditional Diffusion Models for Sequential Recommendation"}, {"review_id": "PaOfV9l70n", "reviewer": "Reviewer_AK4H", "summary": "This paper focuses on the diffusion-based multi-step recommendation. The authors first define a User Behavior Trajectory Prediction (UBTP) task, which aims to predict the next $k$ items based on the user's historical interactions and the predicted $K$ candidate items at each timestep. The authors then propose a novel Listwise Preference Diffusion Optimization (LPDO) method, which consists of three components: (1) the denoising loss, (2) the regularization (prior matching) loss, and (3) the ListPref loss. Experiments on three datasets validate the effectiveness of LPDO for the UBTP task.", "questions": "**Major Concerns:** I have some major concerns as follows:\n\n- **UBTP Task.** This paper introduces a new UBTP task, i.e., $K$-candidate recommendation at the next $k$ steps. While this task is considered novel, the motivation of introducing multi-step recommendation is not well justified. The authors argue that the next-item prediction tends to be short-sighted. However, the autoregressive nature of next-item prediction makes it scalable to multi-step recommendation.\n- **LPDO Method.** The proposed LPDO method is based on the Plackett-Luce model (7). However, I have some concerns: (i) Why not simply use the Top-1 Luce's Choice model? There is only one positive item at each step, and the signal from the 2 to $K$-th items is considered useless for the final objective (20). (ii) It seems that the LPDO method is dependent on $K$, i.e., the number of candidate items at each step. For different metrics, e.g., SeqNDCG@$K$, the $K$ should also vary accordingly. However, there is no description of how to set $K$ in the ListPref loss (11), nor any corresponding experiments.\n- **Next-item Prediction.** From my understanding, the next-item prediction is essentially a special case of UBTP with $k = 1$. Since this task is more widely studied, the authors should also report the performance of next-item prediction in the experiments.\n- **Baselines.** As this paper focuses on the UBTP task, the authors should also provide stronger baselines specifically designed for UBTP. For instance, SASRec can be easily extended to UBTP by incorporating the Plackett-Luce model instead of the Top-1 softmax. The multi-step recommendation can also be achieved in SASRec by changing the embedding size from $d$ to $k \\times d$ and predicting the next $k$ items at each step. These baselines should be compared against the proposed LPDO method.\n- **Discussion on Existing Methods.** The authors do not provide a comprehensive comparison with existing methods. I recommend the authors to compare LPDO with existing autoregressive recommenders (e.g., SASRec) and diffusion-based recommenders (e.g., PreferDiff, DCRec) on the UBTP task (with $k = 1$ and $k > 1$, respectively).\n\n**Minor Comments:** There are some minor issues/questions that do not affect the overall quality of the paper, including:\n\n- Line 237: There are only three datasets in Table 1, but the text mentions four datasets.\n- Line 466: Some typos of $\\mathcal{H}$ in Appendix D.3.", "limitations": "Yes.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\n- The authors propose a novel UBTP task that differs from the traditional next-item prediction task.\n- The authors introduce several new metrics, including SeqMatch@$K$, SeqHR@$K$, and SeqNDCG@$K$, to evaluate the performance of UBTP.\n- The proposed LPDO method is well-designed with rigorous theoretical derivation, achieving superior empirical performance.\n\n**Weaknesses:**\n\n- The motivation of the new UBTP task is not well justified. In other words, why the multi-step is better than the next-item prediction task?\n- The necessity of introducing the Plackett-Luce model is also not well justified. Why not simply use the Top-1 Luce's Choice model instead?\n- The performance of next-item prediction is not reported, while it is essentially a special case of UBTP with $k = 1$.\n- The baselines are not specifically designed for UBTP, and the comparison with existing methods is limited.\n- Lack of comprehensive comparison and discussion with existing methods, e.g., SASRec and DCRec.", "was_revised": true, "final_justification": "The authors' response has addressed my concerns. However, there are still many unclear statements in the paper, such as the inconsistent use of notation, the lack of clarity in the experimental settings, and insufficient explanation of the baseline methods (especially the modified ones). Although I have given a Borderline Accept, I believe that the paper still requires substantial revision to meet the standards for publication.", "rebuttal": "Thank you for your time and effort in reviewing our paper! We sincerely appreciate your thoughtful feedback and hope that our responses effectively address your concerns and support a score revision.\n\n> W1&Q1: The motivation of the new UBTP task is not well justified. In other words, why is the multi-step is better than the next-item prediction task? \n\nThank you for the question regarding the motivation behind introducing UBTP. While autoregressive next-item prediction can technically be extended to multi-step forecasting by rolling out one prediction at a time, we argue that this greedy, locally optimized generation strategy fails to capture global coherence and long-term dependencies inherent in user trajectories. We try to analyze it from four distinct perspectives:\n\n- **Cascading Error and Exposure Bias:** Autoregressive rollout conditions each future prediction on previously generated items. Errors early in the sequence can propagate, degrading the quality of later predictions [1]. This is particularly problematic in recommendations, where early inaccurate suggestions can distort the entire predicted interaction path.\n\n- **Lack of Global Preference Modeling:** Next-item models optimize local pointwise or pairwise objectives. In contrast, user trajectories are structured objects, where preferences emerge not only at the item level but also from inter-item dependencies, topic continuity, or progression (e.g., watching a trilogy or completing a course). These are not captured by locally greedy methods.\n\n- **Empirical Evidence:** As shown in Tab.1, even strong autoregressive models like SASRec-ar underperform on long-sequence prediction metrics (e.g., SeqMatch), validating that non-autoregressive, trajectory-level modeling yields better alignment with real-world behavior.\n\n- **Non-Autoregressive Benefits:** Our formulation enables parallel generation of full-length trajectories with listwise supervision, offering better sample diversity and efficiency compared to autoregressive alternatives.\n\nTherefore, UBTP is not just a repackaging of next-item prediction, but a principled extension that acknowledges and addresses the limitations of autoregressive rollout when the goal is to model user behavior as a coherent, causally evolving sequence.\n\n--- \n\n> W2&Q2(i):  Why not simply use the Top-1 Luce's Choice model?\n\nThank you for your thoughtful questions. The introduction of the Plackett–Luce (PL) model is a key design choice motivated by the need to capture global preference structures over full-length trajectories. While simpler alternatives like Top-1 Luce’s Choice model local preference signals, they fail to supervise the relative ordering among multiple relevant items.\n\nSpecifically, the PL model allows us to optimize the likelihood of the entire ordered item sequence simultaneously rather than focusing on the top-ranked item at each prediction step. This is essential because in our UBTP task, user preference across future steps exhibits significant ordering constraints and interdependencies. In contrast, the Top-1 model ignores the dependencies among subsequent positions beyond the top-ranked item [2-4], reducing its ability to produce coherent long-term user trajectories. Furthermore, the suggested Top-1 Luce's Choice model essentially corresponds to our baseline method, SASRec-AR [5], in the experiments, where predictions are optimized individually and independently at each step of the sequence. \n\nOur experiments consistently show significant performance gains from the PL loss compared to the position-wise baseline methods (including SASRec-AR). LPDO achieves substantial improvements in all evaluation metrics, demonstrating that explicitly modeling the full-sequence ranking structure is necessary and beneficial for accurate multi-step user behavior prediction.\n\n---\n\n> W2&Q2(ii): It seems that the LPDO method is dependent on K, i.e., the number of candidate items at each step. For different metrics, e.g., SeqNDCG@K, the K should also vary accordingly.\n\nWe would like to clarify that LPDO is not dependent on the number of candidate items at each step. During the optimization process, LPDO interacts with all candidate items for optimization without negative sampling. Specifically, the ListPref loss itself is formulated to consider the full candidate set, and its computation is independent of the evaluation metric. \n\nRegarding evaluation metrics, following traditional sequential recommendation settings [5-7], the value of K in metrics such as SeqNDCG@K is determined by the evaluation protocol and does not affect the training procedure or the ListPref loss (Eq.11). In our experiments, we follow standard practice by reporting results for multiple values of K (e.g., K=5, 10, 20), and these are clearly specified in the experimental section.\n\n---\n\n> W3&Q3: From my understanding, the next-item prediction is essentially a special case of UBTP with k=1. Since this task is more widely studied, the authors should also report the performance of next-item prediction in the experiments.\n\nThanks for your insightful feedback. Indeed, next-item prediction is a special case of UBTP when the prediction length k = 1, and it corresponds to the widely studied task of Sequential Recommendation (SR). UBTP requires the model to generate a coherent sequence of future interactions, capturing inter-item dependencies and preference evolution over multiple steps, which are not addressed in standard next-item recommendation settings. \n\nTo address the reviewer’s concern, we report the performance on the first position of the predicted trajectory (i.e., the first item among the multi-step prediction) using models trained under the UBTP setting. This provides a reference point that overlaps with next-item prediction. We report the performance on the first position (i.e., the next item) from the predicted trajectory. The results on MovieLens-1M (len=5), evaluated by HR@5 and NDCG@5, are shown below:\n\n|Metric|SASRec|STOSA|DiffuRec| DCRec|LPDO|\n|-|-|-|-|-|-|\n| HR@5|0.0921|0.0912|0.1052|0.1293|0.1571|\n| NDCG@5|0.0518|0.0506|0.0621|0.0710|0.0866|\n\nLPDO achieves the highest performance on the first predicted item, suggesting that even when evaluated on short-horizon prediction, the model trained for UBTP generalizes well. We will include these results in the appendix of the revised version.\n\n---\n\n> W4&Q4: As this paper focuses on the UBTP task, the authors should also provide stronger baselines specifically designed for UBTP.\n\nThank you for your insightful suggestions. We would like to clarify that in our experiments, we have already extended SASRec to support UBTP by applying the Top-1 softmax at each prediction step (as SASRec-ar), enabling multi-step recommendation. This approach aligns with the UBTP setting and provides a fair baseline for comparison. \nBesides, we include sequential recommendation baselines such as DiffuRec and DreamRec, which have been widely used and offer valuable points of comparison. These baselines help demonstrate the effectiveness of our method.\n\nRegarding the embedding size, our implementation does not require changing the embedding dimension from d to d×k. Instead, the search space expands from d to $d^k$, where d is the number of candidate items and k is the prediction length. This design ensures that the model can generate listwise predictions without modifying the underlying embedding structure.\n\nRegarding incorporating the Plackett-Luce optimization ($\\gamma=0.5$) with SASRec, we report the performance comparison below:\n\n| Model|SHR@5↑|SNDCG@5↑|SHR@10↑|SNDCG@10↑|SMatch@50↑|SMatch@100↑|PPL↓|\n|-|-|-|-|-|-|-|-|\n|SASRec|0.0805|0.0453|0.1364|0.0573|0.1045|0.2009|33.62|\n|SASRec+PL (γ=0.0)|0.0824|0.0486|0.1446|0.0617|0.1143|0.2265|32.83|\n|SASRec+PL (γ=0.3)|0.0852|0.0480|0.1469|0.0624|0.1139|0.2230|32.60|\n|SASRec+PL (γ=0.5)|0.0867|0.0487|0.1473|0.0626|0.1152|0.2286|32.12|\n|SASRec+PL (γ=0.8)|0.0848|0.0473|0.1468|0.0620|0.1128|0.2192|32.12|\n|LPDO|0.1218|0.0679|0.1983|0.0825|0.1559|0.2796|30.36|\n\nThis experiment shows that incorporating PL optimization brings performance improvements to existing models such as SASRec. However, LPDO still outperforms these variants by a clear margin across all metrics, demonstrating that our method benefits not only from listwise supervision, but also from its integration into the diffusion-based trajectory modeling framework.\n\n---\n\n> W5&Q5: Discussion on Existing Methods. The authors do not provide a comprehensive comparison with existing methods. I recommend the authors to compare LPDO with existing autoregressive recommenders (e.g., SASRec) and diffusion-based recommenders on the UBTP task (with K=1 and K > 1).\n\nThank you for raising this point. In our experiments, we include SASRec with autoregressive mode (denoted as SASRec-ar), as well as diffusion-based baselines such as DiffuRec and DCRec. We provide the comparion results of K=1 in the response of W3&Q3, please refer to it. As for results of K=3/5/10, please refer to Tab.1.\n\nWe appreciate your feedback. If there are additional aspects you would like us to elaborate on, we are happy to provide further analysis.\n\n---\n\n> Q6: Typo at Line 237 and 466\n\nThank you for pointing out. We will revise the manuscript to correct this.\n\n\n[1] Limitations of Autoregressive Models and Their Alternatives\n\n[2] Fast and accurate inference of Plackett–Luce models  \n\n[3] Plackett-Luce model for the learning-to-rank task    \n\n[4] RankDistil: Knowledge Distillation for Ranking      \n\n[5] Self-Attentive Sequential Recommendation \n\n[6] DiffuRec: A Diffusion Model for Sequential Recommendation\n\n[7] Generate What You Prefer: Reshaping Sequential Recommendation via Guided Diffusion"}]

Author rebuttal:

Meta-review: The paper introduces User Behavior Trajectory Prediction (UBTP), which forecasts coherent multi-step user interaction sequences rather than only the next item. To address this task, the authors propose Listwise Preference Diffusion Optimization (LPDO), which integrates Plackett–Luce listwise supervision into diffusion training through a variational bound. The paper also introduces a new metric, SeqMatch, designed for strict trajectory-level evaluation. Experiments on multiple benchmarks demonstrate consistent improvements over both strong sequential baselines (e.g., SASRec, DCRec) and diffusion-based baselines (e.g., DiffuRec).

The strengths are the clear formulation of UBTP as a distinct task (Reviewer AK4H initially questioned but accepted after rebuttal), the principled integration of listwise ranking into diffusion ELBO (Reviewer EHty), and strong empirical results across datasets (Reviewer ULMe, Reviewer WfsB). Ablations provided during rebuttal clarified the contributions of the loss and causal transformer, which addressed novelty concerns (Reviewer WfsB).

The weaknesses are clarity and notation issues (e.g., “UBTM” instead of “UBTP” -- Reviewer EHty, Reviewer AK4H), performance degradation on longer horizons (Reviewer EHty), sensitivity to hyperparameters (Reviewer EHty), and initially incomplete baseline comparisons (Reviewer AK4H, later partly addressed). Reproducibility was also initially a concern due to lack of code release, though the authors committed to providing it (Reviewer ULMe).

During discussion, most concerns were clarified: novelty and ablations satisfied Reviewer WfsB; code/statistical issues were resolved for Reviewer ULMe; Reviewer AK4H raised but then accepted the motivation and baseline coverage; Reviewer EHty did not re-engage after rebuttal. Overall, the contribution is original, technically solid, and empirically convincing despite remaining presentation issues.

Final Recommendation: Accept
Decision: Accept (poster)