Discrete Diffusion for Bundle Construction
Authors: Teng Tu
Ai Li
Yunshan Ma
Shuo Xu
Xiaohao Liu
Haokai Ma
Liang Pang
Tat-Seng Chua
Venue: ICLR 2026 Poster (2026)
Keywords: Bundle Construction
Bundle Completion
Recommendation System
Discrete Diffusion Model
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: As a central task in product bundling, bundle construction aims to select a subset of items from large item catalogs to build an entire bundle or, more practically, complete a partial bundle. Existing methods often rely on the sequential construction paradigm that predicts items one at a time, nevertheless, this paradigm is fundamentally unsuitable for the essentially unordered bundles. In contrast, non-sequential methods model a bundle as a set, but still face two dimensionality curses: the combinatorial space grows exponentially with both bundle length and catalog size. Accordingly, we identify two technical challenges: 1) how to effectively and efficiently model the higher-order intra-bundle relations with the growth of bundle length; and 2) how to learn item representations that remain discriminative while avoiding search directly over a huge item catalog.

To address these challenges, we propose DDBC, a Discrete Diffusion model for Bundle Construction. DDBC leverages a masked denoising diffusion process to build bundles non-sequentially, capturing joint dependencies among items without relying on a fixed decoding order, thereby partially alleviating the combinatorial challenge introduced by increasing bundle length. To mitigate the curse of large catalog size, we integrate residual vector quantization (RVQ), which compresses item embeddings into discrete codes drawn from a globally shared codebook, enabling more efficient search while retaining semantic granularity.  We evaluate our method on real-world bundle construction datasets of music playlist continuation and fashion outfit completion, and the experimental results show that DDBC can achieve more than 100\% relative performance improvements compared with state-of-the-art baseline methods. Ablation and model analyses further confirm the effectiveness of both the diffusion backbone and the RVQ tokenizer, with gains becoming more pronounced for longer bundles and larger catalogs. Our code is available at https://github.com/241416/DDBC.

Published as a conference paper at ICLR 2026
DISCRETE DIFFUSION FOR BUNDLE CONSTRUCTION
Teng Tu 1 Li AiRt, Yunshan Ma Shuo Xu Xiaohao Liu', Haokai Ma', Liang Pang". Tat-Seng Chua'
National University of Singapore,
2 Key Laboratory of AI Safety, Institute of Computing Technology, CAS,
Singapore Management University, Shandong University
Equul contribution. Coorrespnnding author.
ABSTRACT
As central task in product bundling, bundle construction aims to select subset of items from large item catalogs to build an entire bundle or, more practically, complete partial bundle. Existing methods often rely the sequential con- struction paradigm that predicts items one at a time, nevertheless, this paradigm is fundamentally unsuitable for the essentially unordered bundles. In contrast, non-sequential methods model a bundle as a set, but still face two dimensional- ity curses: the combinatorial space grows exponentially with both bundle length and catalog size. Accordingly, we identify two technical challenges: 1) how to effectively and efficiently model the higher-order intra-bundle relations with the growth of bundle length; and 2) how to learn item representations that remain discriminative while avoiding search directly over huge item catalog.
To address these challenges, we propose DDBC, Discrete Diffusion model for Bundle Construction. DDBC leverages a masked denoising diffusion process to build bundles sonueequunt,llly, capturing joint dependencies among items without relying on a fixed decoding order, thereby partially alleviating the combinatorial challenge introduced by increasing bundle length. To mitigate the curse of large catalog size, we integrate residual vector quantization (RVQ), which compresses item embeddings into discrete codes drawn from globally shared codebook, en- abling more efficient search while retaining semantic granularity. We evaluate our method on real-world bundle construction datasets of music playlist continua- tion and fashion outfit completion, and the experimental results show that DDBC can achieve more than 100% relative performance improvements compared with state-of-the-art baseline methods. Ablation and model analyses further confirm the effectiveness of both the diffusion backbone and the RVQ tokenizer, with gains becoming more pronounced for longer bundles and larger catalogs. Our code is available at
com/ 24//21/444111/00
INTRODUCTION
Product bundling has been a pervasive business strategy, which originates from conventional retail- ing, evolves e-commerce, and is further adopted by generic online services, such music and video streaming (Chang et al. 2020). A product bundle is a set of relevant items assembled to satisfy users' needs (e.g., games, outrits, playlists, meal kits) (Sun al. ing sellers' pursuit. Bundle construction, i.e., select subset of items from the large item pools to build an entire bundle or complete a partial bundle, is the first and foremost problem among various bundle-centric studies, such personalized bundle recommendation (Ma et al. (022).
2024a) and promote sales regard-
Existing studies, either specifically designed for bundle construction (Han et al. 2017 Bai et al.) 2019 Gong et al.) 2019; Deng et al. [021] general sequential recommendation (Kang & McAuley 2018 Sun et al. 2019). have an important yet often overlooked flaw: most of them based sequential construction paradigm, i.e., predict the next item only rather than all the items in the entire bundle, however, such a sequential construction paradigm is essentially not suit- able for bundle construction. Intuitively, bundle is not sequence of user's interacted items, and

---

Published as a conference paper at ICLR 2026
user is not necessarily follow certain sequential order to consume the items within a bundle ! Thereby, sequential dependencies barely exist between consecutive items in a bundle, and sequential models bring marginal benefits to bundle construction. Delving deep into the technical foundations, consider N as the total number of items (item catalog size) and & as the bundle length (number of items within bundle), the theoretical space of modeling bundle a sequence is the permuta- tion, i.e., P(N, k), while modeling it as a set by relaxing the sequential constraint will significantly downgrade the space to the combination, i.e. C(N, k). Nonetheless, simply discarding the sequen- tial construction paradigm, e.g., existing non-sequential construction methods (Tomasi et al. 2024] Yang et al., 2024). only partially addresses the problem, since the space of the combination still exponential to item catalog size N and bundle length kt which we call the two dimensionality curses.
These two dimensionality curses induce two technical challenges: First, bundle construction re- quires to model the intra-bundle relations, such similarity, compatibility, composability, etc. among any possible combinations of items, e.g. pair-wise, tripartite, and quaternary (Chang et al.] 2020). Thus, how to effectively and efficiently preserve these higher-order relations, considering that the complexity increases exponentially with the linear growth of k; remains the first key challenge. Second and more seriously, the item catalogs, from which draw items to build the bundle, often huge. For example, .N could be tens of thousands or even millions on some online platforms such as Spotify or Amazon. Conventional approaches typically leverage one embedding for each item (Ma et al.] 2024c), consequently, it is highly difficult to navigate through the huge candidate space and precisely pick the desired item for certain bundle. Therefore, how to learn item embed- dings that are sufficiently discriminative regarding different bundling functions while maintaining a relatively small search space poses the second technical challenge.
To tackle the above two challenges, we propose a method that leverages Discrete Diffusion for Bundle Construction, named as DDBC. Specifically, to model the higher-order intra-bundle item relations, we introduce diffusion model as the backbone to replace the previous sequential or non- sequential solutions. Basically, the diffusion model features with a non-sequential construction paradigm, where it picks items according to the learned strategies regarding the entire bundle struc- ture instead of following a certain pre-defined left-to-right sequential order. In terms of the second challenge caused by huge item catalog size, we leverage the residual vector quantization tokenizer (RVQ) to quantize the continuous item embedding into multiple discrete codes (Rajput et al.) 2023), The codes of each item are selected from globally shared codebook that is significantly smaller than the original item set, remarkably relaxing the dimensionality curse caused by N. By integrat- ing the RVQ tokenizer into the diffusion backbone, Concretely, we treat complete bundle b as the clean state at /=0; at each forward step we randomly mask subset of positions, eventually reaching an all- [MASK]. The training objective is learn the reverse denoising dynamics pe (b; b,, t). During inference, given partial bundle with unknown slots marked [MASK], we iteratively denoise until the bundle is fully recovered. Importantly, ran- dom masking exposes the model to rich contexts during training, thereby approximating the joint distribution modeling over bundle items and providing the flexibility to accommodate different de- coding priors. Also, the item codes learned by RVQ have different levels of semantic granularity, therefore, the diffusion model can learn the bundling strategy more fine-grainedll.
design our discrete diffusion model DDBC.
Our contributions include: (1) We emphasize bundle construction should follow non-sequential construction paradigm than with a fixed decoding order, and instantiate this view with a masked denoising process. (2) We operate the diffusion model in vector-quantized discrete space using RVQ, which relaxing the dimensionality curse caused by huge item catalog size. (3) We provide extensive empirical evidence that our approach outperforms baselines in bundle construction, with benefits especially pronounced on larger bundles and larger item catalogs. Comprehensive ablation and model studies further verify the contribution of each component.
2 RELATED WORK
We review three lines of literature most relevant to our work: bundle construction, generative rec- ommendation, and discrete diffusion models.
Some hundles may have a sequential order by design, while here we focus on the general scenarios.
2

---

Published as a conference paper at ICLR 2026
Bundle construction is the task of selecting subset of items from the large item pools build an entire bundle or complete a partial bundle. It typically comprises two parts: (1) an encoder
for users, items, and bundles, and (2) bundle generator. On the encoder side, early advances fuse
semantics feature (often via multimodal encoders e.g., Elizalde al. (2023); :
[ [i ( (2023);
Radford
et al.] (202T); Liu et al. (2025b)) with collaborative signals (Sarwar al. 2001 He al. 2020) to
learn stronger item embeddings (Ma et al. 2022; 2024a bj Salganik et al. 2024). However, these
encoders do not directly capture bundle-level structure; semantically similar items may still not co-occur, whereas real user-constructed bundles balance relevance, exhibit diversity, and maintain complementarity (Sun al. 2024a). Most bundle generators still follow a sequential construction
paradigm (Chen et al. 2019 Bai et al. 2019 Chang et al. 2021 Deng et al. 2021 Liu et al. 2025a Han et al. 2017 Sun al. 2024b). however, the item order within a bundle does not necessarily reflect how users construct or consume bundles. Relying on fixed order can introduce unnecessary
order bias and harm generalization by overfitting to dataset-specific sequences (Yang et al. 2024).
Several non-sequential approaches have been proposed. |Wei et al. (2022) predicts all bundle items in parallel with a contrastive non-auto-regressiv decoder, but it relies on predefined templates and fixed object types. Tomasi al. (2024) uses continuous-space diffusion model but only accepts text prompts as input. Yang et al. (2024) outputs an order-agnostic set in one shot; however, it lacks explicit intra-bundle relations interactions during generation. More importantly, most of these works generate bundles from scratch and do not address partial bundle completion. Our approach targets this gap via discrete masked denoising. completing the missing items an order-agnostic manner.
Generative recommendation is paradigm that reframes recommendation as generating target item IDs rather than full-rank retrieving (Wu et al. 2024 Li al. 2024a| He et al. 2025). The line originates from generative retrieval (Rajput et al. (023): using residual vector quantization (Barnes) ct al. 1996 Lee et al. [0022). items are quantized into multiple semantic IDs from coarse fine, and an auto-regressive decoder generates these IDs conditioned
context. Subsequent work extends this paradigm to multimodal settings (Liu et al,, 2024a) and LLM backbones (Zheng et al. [024] Zhai et al. 2025). As previously discussed, sequential construction paradigm is not suitable for bundling tasks; accordingly, we retain the multiple semantic-ID idea but replace AR backbone with discrete diffusion model.
Diffusion models learn to generate data by inverting a forward noise process: in continuous spaces they have been widely used for images, audio, and trajectories (Ho et al.) 2020 Janner et al. 2022 Kong et al. [222]] Liu et al. 2023; Yang et al.] 2022). For discrete data, diffusion extends to cate- gorical tokens by corrupting symbols (often to absorbing [MASK]) and denoising to reconstruct them (Austin et al. 202T Sahoo et al. 2024). Within recommendation, diffusion has largely been applied to sequential next-item prediction. operating on item latent embedding space (Wang al.) 2023 Yang et al. 2023 Li et al. 22024b] Liu et al. (0224). while discrete diffusion remains com- paratively underexplored (Lin et al. 2024 Ju et al. 2025). In this work, we adopt an MDLLM-style discrete diffusion backbone and leverage its arder-agnostic nature to better model bundles. To the best of our knowledge, we are the first to study bundle construction with discrete diffusion.
3 METHOD
Our framework consists of two key components: (1) RVQ to discretize item embeddings, and (2) DDM that operates over the code tokens for full bundle construction. The overall architecture is illustrated Figure [
3.1 PROBLEM FORMULATION
I = i2......... in} denote the item catalog and B = (b,, b2, byr the collection of bun- dles, where N and M denote the number of items and bundles, respectively. Fach bundle b E set of items, b = { ........8 Ajp }, (fi....; S [N), b/ 2 2. Each item E I is mapped by feature extractor to a latent vector E(i), where the feature often encapsulates semantic signals and collaborative. filteriini signals depending on the datasets. We formulate the bundle construction task as: for bundle b. given a partial bundle b C b, predict the rest part of the bundle (the com- plementary item set) b, = \ b.- The same formulation also supports scrrtc construction by setting b,, 0.
........y
3

---

Published as a conference paper at ICLR 2026
Item Tokenization
Mask Discrete Diffusion Modeling
Illustration
Bundle
Training
Tull Burgli
Encoder
C04
bxi
bei
bel
Diffusion Transformers Denoiser
inoutpartio bundle
kona poprodict
RVQ
P
Ivl
Pvd
Exi
Iack
Exi
Iet
Inference
Ramm codes
Flagg tokee
Mank token
Forward comuption
Reveras denoising
Figure 1: The overall framework of DDBC. The left side illustrates the item tokenization process via RVQ. The right side visualizes the training and inference stages of the masked discrete diffusion modeling. To be noted, we only show the forward process of the training stage, of which the back- ward process is just reverse of the forward and omitted for simplicity.
3.2 RESIDUAL QUANTIZATION OF ITEM EMBEDDINGS
To make masked discrete diffusion feasible on large catalogs, we first discretize continuous item embeddings into compact, hierarchical code space via RVQ. We apply an L-level RVQ to obtain tuple of discrete code indices z(i) = (Zi.1..... 2. The last level is a dedup code that carries no semantics and acts purely as an iuto-increment field to ensure one-to-one mapping from code tuple back to unique item ID. The level order is fixed rather than permutation--qquivllentt each level is learned on a different residual stage and therefore plays a distinct role the code tuple. Formally, ž E (+) is a discrete index token for the l-th codebook, where V(4) A (1...., C₂} ] and Ct | It selects codeword in (()) {ef() ..... c Rd. We view the model vocabulary as disjoint union across levels, V A I
(0)
P=1 V(e), so token is always interpreted together with its
level. Let the residual be r()) Ei)) and, for & = 1. L.
Zi,6 = arg min [[((_]) !
(0)) = r (t-1) !
(1)
eEVEE)
The reconstruction uses only the semantic codebooks: É()) = Σドー S., Early codebooks cap- ture coarse semantics; later residual codebooks refine details, inducing semantic smoothness among similar items. We train the codebooks with an RVQ loss that combines a reconstruction term and a codebook commitment term:
L-1
LRvQ ||E()) B(I)
+ 8 2 (g(rr((1))
- 1 -glle_))s
(2)
where sgl-] denotes stop-grad gradient and 33 balances the commitment loss. We use a ttraight-through estimator for the discrete assignment; codebooks are updated via gradient descent.
For a bundle (l....,Ce) C:): the j-th row contains the codes representing item iz.
(i....., ; bb)), RVQ yields token matrix ((0) N b|xL with entries zy.t E
Among many quantization strategies, we choose RVQ for three reasons. (1) Vocabulary compres- sion. Its theoretical capacity is I Ct. enabling small per-level vocabulary to index a very large item universe. (2) Denser supervision. Each item contributes L code tokens; at level E, a code typically aggregates roughly N/C₁ items (for N total items), code-level supervision is markedly denser than item-ID supervision. We quantify the increase in effective supervision in Section 4 (3) Coarse-to-fine granularity of semantics. Hierarchical residual codebooks perform implicit cluster- ing at multiple granularities, which benefits downstream denoising. Additionally, when a candidate set is available in real applications, the finest semantic level and the disambiguation index may be
4

---

Published as a conference paper at ICLR 2026
unnecessary at inference time: decode with fewer RVQ levels and map prefixes to candidate items via an inverted index over code prefixes. We study this design choice in Section
3.3 MASKED DISCRETE DIFFUSION OVER CODE TOKENS
We cast bundle construction a masked discrete denoising process. In contrast to the sequential construction paradigm, this formulation avoids committing to fixed decoding order and instead lets the model condition on the full bundle context. Importantly, our discrete diffusion does not impose strictly set-invarian objective: items are still flattened into list and we do not explicitly enforce permutation invariance. Accordingly, the property should be understood as approximate order-insensittvity rather than exact permutation invariance. In practice, symmetric masking and aggregated supervision expose the model to diverse reveal orders, which makes the learned predic- tions substantially less dependent on absolute positions. To realize this idea, adopt discrete corruption mechanism. The key components are: an
diffusion framework with an absorbing-mas input tokenization design for bundles, a forward corruption process that incrementally masks tokens, a bidirectional Transformer as the reverse denoiser, and an order-agnostic inference procedure with token-level validity constraints.
Input tokenization for bundles. We serialize bundle by inserting <boi> before each item and wrapping with <bos> and <eos>. Let 2j,0 denote the b-th code token of item j (j=l...., [b/, (=1...,, L). We use exactly two index sets:
Sang = { <bos>>, <boi>, <eos>}, Soode = {(i,)) : j -..... |b), (= I,...,,, LJ. (3)
Tokens Qaa are never masked; corruption and prediction operate only on Zj.t with (1 8) E Peode-
Forward corruption. We use absorbing-mass Markov chain as in masked discrete diffusion. At each step & E (L....,T), each currently unmasked token 24.e with (j, E) E Peode is independently replaced by [MASK] with probability Be E (0, 1):
<< (t) (t-1)
Zje = =w)=1 1 Be, (03/20 [MASK]
(t-1) zj + [MASK]] 3b,, (4)
for any token value # [MASK], with the absorbing condition q(2,,e [MASK]
(t-
z
[MASK]) and independence across (j. e). Let a, = -IT'_ - -3,) be the survival probability. The dlosed-form transition from 1=0 to is:
(3)2 v =je = u) = oz 1(v = u| + (1 - a.) 1[c [MASK]],
(5)
i.e, after steps a token either survives with probability ar or is masked with probability 1 - az.
Reverse denoising. A bidirectional Transformer 0 is trained to predict the original token values from a corrupted sequence. At inference, it produces a categorical distribution for each masked position conditioned on the current noisy tokens, the timestep
po
(0) (1
(t)
E A where A | A (pe (0, 10 1pp11}.
(6)
Following common practice in Sahoo et al. (2024), we use the "simple" reconstruction objective that trains pp to predict the original token zj, directly from a state (()) corrupted at a random timestep Crucially, tokens that are unmasked, either because they belong to b, or because they have already been generated in previous step, are treated as clamped observations; they are never masked again and remain fixed in all subsequent steps. This mechanism enables the model to unmask items in any order during generation, without ever overwriting code once it's decided. 2
(0)
Training objective. Let M, C Pente be the set of positions masked by the forward process at step I. The discrete diffusion variational objective reduces to a weighted masked-token cross-entropy:
ENLLO = EE- EM
Σ
-
log pol po(250 (0)
()))).
(..E
While diffusion can he extended to allow re-masking to revise earlier decisions, we do not enable that option here and leave it future work.
5

---

Published as a conference paper at ICLR 2026
Inference. We model bundle construction iterative denoising of partially masked token matrix. Let the observed set be by and the unknown complementary set be by with by items. Denote by S2 the positions (including all RVQ levels) that belong items in b,, by Q2 the positions that belong to items in by: and by Qmag- We construct an input sequence by flattening tokens row-wise and inserting <boi> > before each item's I. tokens to mark boundaries. Let index positions in the flattened token sequence. Formally, the initial state Z is:
zu v E 22 U [mag) The + 1fu E [Gll [MASK].
(8)
Here, Tu represents the given token at position u, with Riag kept unmasked so the model knows item segmentation. The tokens of b remain clamped throughout. After decoding, a predicted item î is obtained by mapping its token tuple back to the catalog or to reconstruction É(i) = - es
Token-validation constraints. At generation time, we constrain the model's predictions to respect the level-wise token sets induced by RVQ codebooks. Specifically, for each position (j, () (code level l of item j), we restrict the predicted token to the level-é token set
zye E V(A A {1,...,
by setting the logits of any token not in (0 to -oo before the softmax. This validation step helps ensure that generated code tuples can be decoded legal catalog items, which crucial for main- taining recommendation feasibility.
EXPERIMENT
4.1 EXPERIMENTAL SETTINGS.
Model settings. We use CLHE (Ma et al. 2024c) as the shared item encoder, i.e., E(i) = CLHE(1), so that performance differences can be attributed mainly to the generative backbone rather than to encoder quality. Unless otherwise noted, our RVQ uses L = 4 levels with fixed per-level codebook size Ce = C. We utilize lightweight DDiT architecture for our Diffusion backbone, with trans- former blocks, each with hidden size of 64 and 8 self-attention heads. The model operates with linear noise scheduler a = 1 t/T. All experiments are performed on four NVIDIA A40 GPUs, and all models are trained in 20,000 steps.
Datasets. Following prior research on bundle construction Ma et al. 2024c Liu et al. (2025a), we evaluate two representative datasets, Spotify (Chen et al.) 2018 and POG (Chen et al.) [2019). Unlike these works, our discrete diffusion model currently requires a fixed number of tokens per instance, so truncate bundles target length. For bundles longer than the target length k; sample a start index s uniformly from {1..... bb k + 1} and keep the contiguous subsequence (i....., is+ This avoids deterministic prefix truncation and reduces bias toward a fixed posi- tional pattern. For the Spotify playlist dataset, we create three subsets by capping playlist length 30/60/90 items appotify=30.600 is small, we start from its denser variant and derive fixed-length version with four items (denoted POG Unless noted, the input-predict ratio the bundle, |b, : |byl are set as 1 : 1, see Ta- ble for other settings. Samples shorter than the target length are dropped. Each dataset is split into train/ validationn/tsst with non-overlapping bundles. We also perform data augmentation by swapping items within the bundle, and the details are describe in Appendix B
For the POG fashion dataset, whose average bundle length
Candidate size. To ensure fair comparability, we evaluate all methods under an identical can- didate set, since many competitive baselines are inherently defined over fixed candidate pool. To standardize the candidate pool, we set candidate ratio / and construct a shortlist S of size p byl by augmenting the ground-truth targets with randomly sampled non-targets: S
by U Random (,, (7)(bb) (b). Unless otherwise stated, we fix p 100 in all experiments.
4.2 BASELINES.
We consider both non-sequential and sequential construction methods as baselines. To isolate the effect of the generative mechanism, all the baselines use the same item features, i.e. pre-trained embeddings via CLHHE (Ma et al. 2024c).

---

Published as a conference paper at ICLR 2026
Table 1: Overall performance comparison between our DDBC and baselines. "XImprov." denotes the relative improvement over the strongest baseline. Best in bold, second best underlined.
Spotify__st Jace
Spotify Juce t
Spotify Jace 1
POG
Model
f
OAS
OAS
f
OAS 1
f
Jace f OAS f
CLHE
0.071
0.039
0.373
0.100
0.054
0.446
0.119
0.065
0.486
0.140
0.096
0.446
Bi-L.TMM
0.124
0.071
0.489
0.062
0.034
0.430
0.047
0.025
0.426
0.035
0.024
0.390
SASRec
0.070
0.043
0.318
0.089
0.054
0.310
0.050
0.029
0.285
0.169
0.468
TIGER
0.093
0.053
0.329
0.129
0.076
0.413
0.123
0.070
0.480
0.213
0.157
0.546
BundleNAT
0.153
0.090
0.454
0.101
0.056
0.438
0.095
0.052
0.446
0.145
0.097
0.462
BundicMLLM
0.046
0.024
0.296
0.045
0.024
0.324
0.052
0.027
0.355
0.070
0.047
0.322
DDBC
0.282
0.176
0.660
0.285
0.178
0.662
0.287
0.177
0.684
0.139
0.098
0.526
SImprov
84.3%
95.6%
35.0%
120.9%
134.2%
48.3%
133.3%
152.9%
40.7%
Non-sequential construction methods. They input the partial bundle by and predict all the items in the complementary set once. CLHE (Ma et al. 2024c): A method that leverages contrastive learning and hierarchical encoder to learn item and bundle representations. To be noted, CLHE was not originally designed to predict all the items in the complementary set, while it follows the typical top-k recommendation paradigm and evaluation protocol. We re-evaluate it against our metrics that are pertinent to entire bundle construction. BundleNAT (Yang et al., 2024]: A non-auto-regressive generator that predicts a set of items in one shot using preference/compatiiiii signals. It was originally used for the task of personalized bundle recommendation instead of bundle construction, adapt it for our task by removing the user inputs.
Sequential construction methods. They follow an auto-regressive construction strategy: initialize So = b,; for j = O..... [by - 1, choose i, = arg max; . sy) and update Sy+1 = U {iy} until | = [b]. where S, is the current selected set after j steps and M(2 8s)) is the model score (or probability) of adding item given 5y. Bi-LSTM (Han et al., 2017): :): It uses bi-directional LSTM to model the bundle as a sequence. SASRec (Kang & McAuley 2018): A Transformer-bas based sequential recommender trained for next-item prediction. TIGER (Rajput et al.) (023): generates items as discrete semantic token sequences with an auto-regressive decoder. BundleMLLLM (Liu finetunes a multimodal I.I. for bundle construction. Its original evaluation based on the multiple-choiee question protocol since it is impossible to input all the candidate items as input due to context limitation of LLMs. Even though this setting is easier than our all all-ranking setting, to be simple, we follow this paradigm and set the candidate set 20.
al. 2025a):
To be noted, many other recommendation models can be adapted as baselines by following the paradigm of either the sequential or non-sequential construction. For example, the baselines imple- mented in Ma et al. (2024c): MultiDAE (Wu et al., 2016), MultiVAE (Liang et al.) 2018), Hyper- graph Yuu al., 2022), and Transformer (Wei et al. 2023). etc. the other advanced sequential recommendation models. However, we do not include them because they either underperform CLHE or are less relevant the bundle-construutton setting.
4.3 EVALUATION METRICS
We report retrieval-based metrics Fl and Jaccard (Jacc) (Manning et al. 2008 Ding et al. 2023 well as latent-space similarity-based metric OAS (Kuhn 1955). Higher Fl, Jace, and OAS indicate better performance. Let by denote the set of predicted items, these metries are calculated by:
F1 = 2PR
Jace = bb, byy bb, U byl
1 OAS = by
max Σ cos (Os()(()E())) (K.))
(9)
P P R
where P 1b, R 16, bbl and P is the optimal matching between items in by and b, and b,
[by
cos(..)) denotes cosine similarity. Previous methods in bundle construction use popular next-item recommendation metrics, such as recall, ndeg, or hit rate (Ma et al.) 2024c). However, these metrics are not suitable in the scenario of full bundle construction, which needs to assess the quality of the predicted entire item set instead of single item. Therefore, we adopt these three complementary set-
7

---

Published as a conference paper at ICLR 2026
Table 2: Effect of input-predict ratio on Spotify, x==t Best in bold, second best underlined.
5/55
10/50
30/30
45/15
Model
F1 T
Jace 1
OAS 1
F1 1
Jace 1
OAS 1
F1 f
Jace f
OAS
F1 f
Jace 1
OAS f
BundleNAT
0.106
0.059
0.443
0.128
0.072
0.463
0.101
0.056
0.438
0.084
0,046
0.359
SASRec
0.119
0.070
0.425
0.131
0.078
0.442
0.089
0,054
0.310
0.095
0,055
0.315
TIGER
0.087
0.050
0.365
0.100
0.059
0.381
0.129
0.076
0,413
0.154
0.091
0.426
DDBC
0.237
0.144
0.637
0.268
0.164
0.664
0.285
0.178
0.662
0.260
0.161
0.614
Improv.
99.2%
105.7%
43.8%
104.6%
110.3%
43.4%
120.9%
134.2%
48.3%
68.8%
76.9%
44.1%
Table 3: Effect candidate ratio on Spotify 6-
Best in bold, second best underlined.
60-
#=10 10
p=20
#=50
/=100
Model
F1
Jace f
OAS
F1 f
Jace
OAS
F1 f
Jace
OAS
F1
Jacc
OAS f
BundleNAT
0.266
0.163
0.508
0.210
0.124
0.485
0.153
0.088
0.464
0.101
0.056
0.438
SASRec
0.292
0.194
0.519
0.200
0.126
0.474
0.200
0.126
0.475
0.089
0.054
0.310
TIGER
0.191
0.151
0.326
0.107
0.080
0.295
0.108
0,081
0.296
0.129
0.076
0.413
DDBC
0,599
0.447
0.763
0.503
0.355
0.727
0.380
0.250
0.689
0.285
0.178
0.662
Improv.
105.1%
130.4%
47.0%
139.5%
181.7%
49.9%
90.0%
98.4%
45. 1%
120.9%
134.2%
48.3%
level metrics to measure bundle-constructtin quality more faithfully than next-item recommendation metries in our setting.
4.4 OVERALL PERFORMANCE COMPARISON
Table shows the overall performance of DDBC compared with baseline methods. First, among the baselines, BundleNAT and TIGER achieve the strongest performance. These results respectively highlight two key component of our model: the non-sequential construction paradigm and the ad- vantages of discretizing items into multiple codes. Second, on the Spotify dataset series, DDBC clearly outperforms all baselines, achieving 152.9% improvement in Jace on Spotify More- over, the performance gain of DDBC becomes more pronounced as the hundle sequence length increases. These results demonstrate that DDBC effectively captures the higher-order intra-bundle item relations, particularly for long-sequence bundles with rich structural dependencies. Third, on POG our model does not outperform TIGER. fact, since we only predict two items, the task, to some extent reduces to a next-item prediction scenario, where ruto-regeeseive methods such as TIGER have clear advantage.
4.5
MODEL STUDY
Effeet of input-predic ratio. We conduct experiments with different input-predict ratio on Spotifys-en and report results in T We observe that DDBC outperforms all baselines across different partial bundle sizes and exhibits relatively consistent performance, demonstrating its ro- bustness in scenarios with limited known items. Specifically, when the known partial bundles are small (e.g., 5/55, 10/50, 30/30), DDBC achieves substantial improvements over the best baseline by 106%, 1 110% 143% on Jaccard, respectively. Although the performance gap narrows down as the number of input items grow, our method continues to maintain leading position. These re- sults highlight that DDBC is capable of generating coherent and distribution- bundles even when only small subset of items is provided, validating the effectiveness of our masked denoising formulation and the discrete diffusion mechanism.
Effect of candidate ratio. We report the results for DDBC and the baselines under different candi- date ratios in Table 3 The results indicate that while the absolute values of the evaluation metrics fluctuate as the candidate ratio (p) increases, the relative improvements of DDBC over all baselines remain consistently substantial. Interestingly, among basclines, when increases, TIGER starts to bypass other baselines on Fl and Jace (p=100). This can be attributed to the fact that RVQ allows precise reconstruction of item IDs, implying the advantages of using RVQ. These findings highlight the adaptability of DDBC under varying candidate pool sizes, demonstrating its ability to maintain strong bundle representations even when the retrieval space becomes more challenging.
Efficiency analysis. We record the inference time and paremeter size of DDBC and the baseline methods, reported in Figure? where the circle radius indicates each model's overall perfor-
8

---

Published as a conference paper at ICLR 2026
Table 4: Ablation study of key components.
Table Effect of RVQ levels.
Variant
F1
Jace
OAS
E
F1
Jacc
OAS
Our proposed DDBC
0.282
0.176
0.660
(1)
0.182
0.108
0.556
w/o RVQ
0.021
0.011
0.557
(1.2)
0.224 0.136
0.589
w/o boi token
0.176
0.104
0.538
{1, 3}
0.240 0.148
0.590
w/o data augmentation
0,254
0.158
0.599
Our proposed
DDBC
w/o token validity filter
0.276
0.173
{1, 2, 3, 0.282 0.176
0.660
mance. The inference time is measured on Spotifyk- Specifically, although Bi-LSTM has fast inference and smallest parameters, its performance not competitive (see Table DDBC is highly parameter-effiieet, containing only 0.79M parameters, and is significantly smaller than other base- lines. Moreover, DDBC's inference speed is comparable to the one-shot generation method Bundle- NAT and faster than all other baseline models; in particular, it is substantially faster than BundleM- LLM, which relies on interactions with large language models.
4.6 ABLATION STUDY
Key components. To fur- ther evaluate the effectiveness of key components of our model, we conduct ablation experiments (Table 4 as- sess the contribution of each design choice in DDBC. Con- sidering the resource and time overhead imposed by the ex- tremely large vocabulary in Spotify (254,155), perform- ing ablation studies without RVQ would be prohibitively expensive. Therefore, we adopt Spotify the short- est sequence setting. as a more practical benchmark for these experiments.
7.5 x 10
Inferance time [ms/bundle]
Bund
7x
x.5 10
60
CLIE
TIGER
SASRec
20
DDBC
BundleNAT
10"
10
10a
10'
10'
Parameter size [million]
Figure Illustration of the model efficiency comparison. The x-axis is parameter size (millions), the y-axis is infer- ence time (ms/bundle), and bubble radius corresponds to overall performance (larger is better).
We study how each component contributes performance: hierarchical (coarse-to-fine) decoding, token validity filter, boi token, data augmentation, we also investigate how different RVQ depth affect performance. We derive the following insights. (1) Removing RVQ results in dramatic performance drop. We encode items using their IDs and initialize their embeddings with CLHE features, results in dramatic drop in both F1 and Jaccard. This demonstrates RVQ mitigates the dimensionality curse due to N, which crucial as permits dense supervision. (2) Discarding the boi token leads to performance decline. Since Diffusion's generation lacks inherent sequence, integrating the boi token is necessary to guide the model with positional information. (3) Data aug- mentation shows beneficial for modeling. The results of training the original dataset show a slight performance reduction in this case, and simple data augmentation remains significant for diffusion modeling because it explicitly provides richer input context. (4) The token validity filter remains essential to guarantee the validity of the generated bundles, despite its removal leading to only marginal decrease performance. We evaluated the necessity of the token validity filter during inference. While removing the filter resulted in only marginal decrease in overall performance, the invalid ratio concurrently rose to 2.5%. Therefore, the filter remains essential to guarantee the validity of the generated bundles.
To investigate the impact of the item embedding quantization level on model performance as dis- cussed in method section, with fixed 4 levels RVQ, train DDBC with utilizing different levels of RVQ. We report the results Table 5] As the number of RVQ levels used increases, the model captures increasingly finer-grained item information, leading substantial improvements in all the

---

Published as a conference paper at ICLR 2026
evaluation metrics. We state that the current setting represents favorable trade-off between the representational capacity and compression ratio of RVQ.
5 CONCLUSION
We recast bundle construction with masked discrete diffusion model that progressively resolves unknown items in an order-insensitive manner. Conceptually, the formulation addresses the dual dimensionality challenges of bundle construction: (i) it removes the need to commit to fixed de- coding order, reducing the search space from permutations combinations while better preserving higher-order item relations; and (ii) it shrinks the effective search space by mapping items to codes drawn from globally shared codebook. Empirically, coupling DDM with RVQ yields consistent gains over prior sequential and non non-sequential construction basclines, with especially strong im- provements as bundle length grows.
Discussion. Our current instantiation is trained under a fixed-length protocol. While Appendix C,3 shows that DDBC already supports several training-fre free variable-length generation strategies, more principled stopping criteria and explicit length control remain open. Personalization is currently mediated by frozen encoders for user item signals and item semantics; introducing explicit con- ditioning into the diffusion process (e-g., context features user instructions) could yield more user-specific bundling- The RVQ design space (e.g., number levels, codebook sizes, and training regimes) also deserves further study balance identifiability, compression, and semantic smooth- ness. Evaluation also remains imperfect: our current protocol relies on random candidate pool for comparability with sandidate-conditionn metrics, but this only partially reflects the open-world nature of bundle construction where multiple item substitutions may be equally valid beyond a restricted pool; developing evaluation procedures that better capture solution diversity while remaining reproducible is an important direction. Finally, diffusion schedules and inference policies merit deeper optimization: adaptive timestep schedules, selective re-masking strategies, and entropy-guides decoding may further improve sample efficiency and robustness.
baselines and for statistical stability of exact-match
ETHICS STATEMENT
We affirm compliance with the ICLR Code of Ethics. Our study addresses bundle construction (e.g., playlists and fashion outfits) and uses publicly available research datasets and splits released by prior work; no personally identifiable information (PII) or sensitive attributes are collected, inferred, or released. The inputs consist of item identifiers and non-sensitive metadata, and our models operate on discretized representations without accessing user profiles. Any code and models we release will be for research use only and will not include copyrighted media proprietary assets.
REPRODUCIBILITY STATEMENT
We make our method reproducible by specifying the full training and evaluation pipeline, including the RVQ configuration, diffusion horizon, architecture, schedulers, and all hyperparameters. We provide a repository[nteet ptttps://github. com our model as well as the evaluation scripts for FI, Jaccard, and OAS. Upon publication, we plan to release checkpoints (where licenses permit) to reproduce all main and ablation results.
including the implementation of
ACKNOWLEDGMENTS
This research was supported by the NExT Research Center; by the Strategic Priority Research Pro- gram of the Chinese Academy of Sciences (CAS) (Grant No. XDB0680302), the National Natural Science Foundation of China (NSFC) (Grant No. 62276248), and the Beijing Nova Program (Grant No. 20250484765); and by the Singapore Ministry of Education (MOE) Academic Research Fund (AcRF) Tier 1 grant.
10

---

Published as a conference paper at ICLR 2026
REFERENCES
Jacob Austin, Daniel D. Johnson, Jonathan Ho, Daniel Tarlow, and Rianne van den Berg. Structured denoising diffusion models in discrete state-spaces. In NeurIPS, pp. 17981-17993, 2021.
Jinze Bai, Chang Zhou, Junshuai Song, Xiaoru Qu, Weiting An, Zhao Li, and Jun Gao. Personalized bundle list recommendation. In WWW, pp. 60-71, 2019.
Christopher F. Barnes, Syed A. Rizvi, and Nasser M. Nasrabadi. Advances in residual vector quan- tization: a review. IEEE Trans. Image Process., 5(2):226 262, 1996.
Jianxin Chang, Chen Gao, Xiangnan He, Depeng Jin, and Yong Li. Bundle recommendation with graph convolutional networks. In SIGIR, pp. 1673-1676. ACM, 2020.
Jianxin Chang, Chen Gao, Xiangnan He, Depeng Jin, and Yong Li. Bundle recommendation and generation with graph neural networks. TKDE, 35()):332-23344)) 2021.
Ching- Wei Chen, Paul Lamere, Markus Schedl, and Hamed Zamani. Recsys challenge 2018: Auto-
matic music playlist continuation. In RecSys, 2018.
Wen Chen, Pipei Huang, Jiaming Xu, Xin Guo, Cheng Guo, Fei Sun, Chao Li, Andreas Pfadler, Huan Zhao, and Binqiang Zhao. Pog: personalized outfit generation for fashion recommendation at alibaba ifashion. In KDD, pp. 2662-2670, 2019.
Qilin Deng, Kai Wang, Minghao Zhao, Runze Wu, Yu Ding, Zhene Zou, Yue Shang, Jianrong Tao, and Changjie Fan. Build your own bundle-a neural combinatorial optimization method. In ACM MM, pp. 2625-2633, 2021.
Yujuan Ding, Y. Mok, Yunshan Ma, and Yi Bin. Personalized fashion outfit generation with user coordination preference learning. Inf. Process. Manag., 60(5):103434, 2023.
Benjamin Elizalde, Soham Deshmukh, Mahmoud Al Ismail, and Huaming Wang. Clap learning audio concepts from natural language supervision. In ICASSP, pp. 1-5. IEFF, 2023.
Yu Gong. Yu Zhu, Lu Duan, Qingwen Liu, Ziyu Guan, Fei Sun, Wenwu Ou, and Kenny Q. Zhu. Exact-k recommendation via maximal clique optimization. In KDD, pp. 617-626. ACM, 2019.
Xintong Han, Zuxuan Wu, Yu-Gang Jiang, and Larry S. Davis. Learning fashion compatibility with bidirectional Istms. In ACM MM, pp. 1078-1086. ACM, 2017.
Xiangnan He, Kuan Deng, Xiang Wang, Yan Li, Yongdong Zhang, and Meng Wang. Lightgen: Simplifying and powering graph convolution network for recommendation. In SIGIR, pp. 639- 648, 2020.
Yingzhi He, Xiaohao Liu, An Zhang, Yunshan Ma, and Tat-Seng Chua. Llm2rec: Large language models are powerful embedding models for sequential recommendation. In KDD, pp. 896-907, 2025.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In NeurIPS, 2020.
Michael Janner, Yilun Du, Joshua B. Tenenbaum, and Sergey Levine. Planning with diffusion for flexible behavior synthesis. In ICML, volume 162 of Proceedings of Machine Learning Research, pp. 9902 9915. PMLR, 2022.
Zheng Ju, Honghui Du, Elias Z. Tragos, Neil Hurley, and Aonghus Lawlor. Diffgr: A discrete diffusion-based model for personalised recommendation by reconstructing user-item bipartite graphs. In ECIR, volume 15574 of Lecture Notes in Computer Science, pp. 246-254. Springer, 2025.
Wang-Cheng Kang and Julian J. McAuley, Self-attentive sequential recommendation. In ICDM, pp. 197-206. IEEE Computer Society, 2018.
Zhifeng Kong, Wei Ping, Jiaji Huang, Kexin Zhao, and Bryan Catanzaro. Diffwave: A versatile diffusion model for audio synthesis. In ICLR. OpenReview.net, 2021.

---

Published as a conference paper at ICLR 2026
Harold W. Kuhn. The hungarian method for the assignment problem. Naval Research Logisties
Quarterly, 2(1-2):83-99) 1955. doi: 10.1002/ma.338000201009
Doyup Lee, Chiheon Kim, Sachoon Kim, Minsu Cho, and Wook-Shin Han. Autoregressive image generation using residual quantization. In CVPR, pp. 11223-1153,, 2022.
Junnan Li, Dongxu Li, Silvio Savarese, and Steven Hoi. Blip-2: Bootstrapping language-image pre-training with frozen image encoders and large language models. In ICML, pp. 19730-19742, 2023.
Lei Li, Yongfeng Zhang, Dugang Liu, and Li Chen. Large language models for generative recom- mendation: A survey and visionary discussions. In LREC-COLING, pp. 10146-10159, ELRA and ICCL, 2024a.
Zihao Li, Aixin Sun, and Chenliang Li. Diffuree: A diffusion model for sequential recommendation. ACM Trans. Inf. Syst., 42(3):66:1-66:222 2024b.
Dawen Liang, Rahul G Krishnan, Matthew D Hoffman, and Tony Jebara. Variational autoencoders for collaborative filtering. In WWW, pp. 689-698, 2018.
Xiao Lin, Xiaokai Chen, Chenyang Wang, Hantao Shu, Linfeng Song, Biao Li, and Peng Jiang. Discrete conditional diffusion for reranking in recommendation. In WWW, pp- 161-169. ACM, 2024.
Han Liu, Yinwei Wei, Xuemeng Song, Weili Guan, Yuan-Fang Li, and Liqiang Nie. Mmgrec: Multimodal generative recommendation with transformer model. CoRR, abs/2404.16555, 2024a.
Haohe Liu, Zehua Chen, Yi Yuan, Xinhao Mei. Xubo Liu, Danilo Mandic, Wenwu Wang. and Mark D. Plumbley. Audioldm: Text-to-audio generation with latent diffusion models. ICML, volume 202 of Proceedings of Machine Learning Research, pp.
PMLR, 2023.
Shuo Liu, Guoqing Hu An Zhang, Hong Qian, and Tat seng Chua. Preference diffusion for recom- mendation. In ICLR, Singapore, 2024b.
Xiaohao Liu, Jie Wu, Zhulin Tao, Yunshan Ma, Yinwei Wei, and Tat-Seng Chua. Fine-tuning multimodal large language models for product bundling. In KDD, pp. 448-858.. ACM, 2025a.
Xiaohao Liu, Xiaobo Xia, KionKiong Ng, and Tat-Seng Chua. Principled multimodal representation learning, arXiv preprint arXiv:2507.17345. 2025b.
Yunshan Ma, Yingzhi He, An Zhang, Xiang Wang, and Tat-Seng Chua. Crosscbr: Cross-view contrastive learning for bundle recommendation. In KDD, pp. 1233-1241, 2022.
Yunshan Ma, Yingzhi He, Xiang Wang, Yinwei Wei, Xiaoyu Du, Yuyangzi Fu, and Tat-Seng Chua. Multiebr: Multi-view contrastive learning for bundle recommendation. ACM Transactions on Information Systems, 42(4):1 2024a.
Yunshan Ma, Yingzhi He, Wenjun Zhong, Xiang Wang, Roger Zimmermann, and Tat-Seng Chua. CIRP: cross-item relational pre-training for multimodal product bundling. InACM MM, pp. 9641- 9649. ACM, 2024b.
Yunshan Ma, Xiaohao Liu, Yinwei Wei, Zhulin Tao, Xiang Wang, and Tat-Seng Chua. Leveraging multimodal features and item-level user feedback for bundle construction. WSDM, pp. 510- 519, 2024c.
Christopher D. Manning, Prabhakar Raghavan, and Hinrich Schütze. Introduction to information retrieval. Cambridge University Press, 2008.
Alec Radford, Jong Wook Kim, Chris Hallacy. Aditya Ramesh, Gabriel Goh, Sandhini Agar- wal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. Learning transferable visual models from natural language supervision. Marina PMLR, 2021.
Meila and Tong Zhang (eds.), ICMI,, volume 139, pp.
12

---

Published as a conference paper at ICLR 2026
Shashank Rajput, Nikhil Mehta, Anima Singh, Raghunandan Hulikal Keshavan, Trung Vu, Lukasz Heldt, Lichan Hong, Yi Tay, Vinh Q. Tran, Jonah Samost, Maciej Kula, Ed H. Chi, and Mahesh Sathiamoorthy. Recommender systems with generative retrieval. In NeurIPS, 2023.
Subham S. Sahoo, Marianne Arriola, Yair Schiff, Aaron Gokaslan, Edgar Marroquin, Justin T. Chiu, Alexander Rush, and Volodymyr Kuleshov. Simple and effective masked diffusion language models. In NeurlPS, 2024.
Rebecca Salganik, Xiaohao Liu, Yunshan Ma, Jian Kang, and Tat-Seng Chua. LARP: language audio relational pre-training for cold-start playlist continuation. In KDD, pp. 2524-2535. ACM, 2024.
Badrul Munir Sarwar, George Karypis, Joseph A. Konstan, and John Riedl. baan- collaborative filtering recommendation algorithms. In WWW, pp. 285-288222 985-295..2 ACM, 2001.
Fei Sun, Jun Liu, Jian Wu, Changhua Pei, Xiao Lin, Wenwu Ou, and Peng Jiang. Bert4rec: Sequen- tial recommendation with bidirectional encoder representations from transformer. In CIKM, pp- 1441-1450. ACM, 2019.
Meng Sun, Lin Li, Ming Li, Xiaohui Tao, Dong Zhang, Peipei Wang, and Jimmy Xiangji Huang. A survey on bundle recommendation: Methods, applications, and challenges. CoRR, 1.5/2411.00344 2024a.
Zhu Sun, Kaidong Feng, Jie Yang, Xinghua Qu, Hui Fang, Yew-Soon Ong, and Wenyuan Liu. Adaptive in-context learning with large language models for bundle generation. In SIGIR, 2024b.
Federico Tomasi, Francesco Fabbri, Mounia Lalmas, and Zhenwen Dai. Diffusion model for slate recommendation. CoRR, abs/2408.06888 2024.
Wenjie Wang, Yiyan Xu, Fuli Feng, Xinyu Lin, Xiangnan He, and Tat-Seng Chua. Diffusion rec- ommender model. In SIGIR, pp. 832 841. ACM, 2023.
Penghui Wei, Shaoguo Liu, Xuanhua Yang, Liang Wang, and Bo Zheng. Towards personalized bundle creative generation with contrastive non-autoregressive decoding. In SIGIR, pp. 2634- 2638. ACM, 2022.
Yinwei Wei, Xiaohao Liu, Yunshan Ma, Xiang Wang, Liqiang Nie, and Tat-Seng Chua. Strategy- aware bundle recommender system. In SIGIR, pp. 1198- 1207, 2023.
Likang Wu, Zhi Zheng. Zhaopeng Qiu, Hao Wang. Hongchao Gu, Tingjia Shen, Chuan Qin, Chen Zhu, Hengshu Zhu, Qi Liu, Hui Xiong, and Enhong Chen. survey on large language models for recommendation. World Wide Web (WWW), 27(5):60, 2024.
Yao Wu, Christopher DuBois, Alice X. Zheng, and Martin Ester. Collaborative denoising auto- encoders for top-n recommender systems. In WSDM, pp. 153-162. ACM, 2016.
Ling Yang, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Yingxia Shao, Wentao Zhang, Ming- Hsuan Yang. and Bin Cui. Diffusion models: A comprehensive survey of methods and applications. CoRR, abs/2209.00 00796,, 2022.
Ming-Hsuan
Wenchuan Yang, Cheng Yang, Jichao Li, Yuejin Tan, Xin Lu, and Chuan Shi. -oo--uutreeressivve personalized bundle generation. Inf. Process. Manag.. 61(5): 103814, 2024.
Zhengyi Yang. Jiancan Wu, Zhicai Wang, Xiang Wang, Yancheng Yuan, and Xiangnan He. Generate what you prefer: Reshaping sequential recommendation via guided diffusion. In NeurIPS, 2023.
Zhouxin Yu, Jintang Li. Liang Chen, and Zibin Zheng. Unifying multi-associations through hyper- graph for bundle recommendation. Knowledge- Based Systems, 105:55 2022.
Jianyang Zhai, Zi-Feng Mai, Chang-Dong Wang, Feidiao Yang, Xiawu Zheng, Hui Li, and Yonghong Tian. Multimodal quantitative language for generative recommendation. In ICLR, 2025.
Bowen Zheng, Yupeng Hou, Hongyu Lu, Yu Chen, Wayne Xin Zhao, Ming Chen, and Ji Ri-Rong Wen. Adapting large language models by integrating collaborative semantics for recommendation. In ICDE, pp. 1435 1448. IEEE, 2024.
13

---

Published as a conference paper at ICLR 2026
A THE USE OF LARGE LANGUAGE MODELS
We used large language models (e.g., OpenAI ChatGPT 5.1, Claude Sonnet 4.5) as an assistive tool for writing polish (grammar, phrasing, and LaTeX formatting), troubleshooting LaTeX errors, and scaffolding non-critical scripts (plotting and small utilities). LLMs did not contribute novel scien- tific ideas, data collection, result selection, and any code snippets suggested by an LLM were reviewed, rewritten where necessary, and validated by the authors. All technical claims, mathemati- cal formulations, and empirical results are the authors' responsibility. LLMs are not listed as authors and have no authorship rights.
B IMPLEMENTATION DETAILS
Dataset statistics. The statistics for the datasets used in experiments are summarized in Table All Spotify series datasets share large item catalog size (N) of 254, 155, with a massive candidate space. Density Spotifyx=30
Spotify x= > Spotify k==00 Conversely, the POG dataset features a substantially smaller item catalog size (N) of 31,217 and contains more consistent number of
bundles across the splits (e.g. Mirain 29, 704). This variation item catalog size and bundle count allows for a comprehensive evaluation of our method's scalability and performance under different data density conditions.
Data augmentation. To improve the model's robustness and prevent overfitting to a particular sequential item order, we employ a data augmentation strategy based on item swapping. Specifically, for each original item sequence, we performed series of adjacent item swaps on copy of the sequence. For the POG dense dataset, we set swap ratio 0.8, and for the Spotify datasets, we used swap ratio 0.4. Subsequently, we randomly sampled fixed-length subsequence (sequence length) from the perturbed sequence, creating a new augmented training instance. This data augmentation enhancement to the diffusion model, fulfilling the non-sequential modeling objective while countering the potential issue overfitting to the certain given sequential order in the bundle.
Over-retrieval. To standardize the evaluation of generative models which can produce multiple possible outputs, we employ an Over-Retrieval Strategy. This strategy aggregates the results from multiple generation attempts, effectively forming the union By used in the retrieval-based metrics. For generative sampling models, we evaluate performance under varying number of attempts 5, 10, 20, 50} (denoted as Multiple Sampling, MS). For auto-regressive baselines that use beam search, we report the results using beam width ò [1,3, 3, 5, 10, 20, 50), mapping the beam width to the number of attempts (K = b) for a fair comparison of computational cost.
Input tokenization for bundles (details). Given
fi.....,4ppl hddp with item codes z(i,)
(2 L,LL), the serialized sequence is
x = (<bos>, <boi>, 21. 2L.L
(10)
item
<boi>, 22,1,... Z2
Item
<boi>, 210,.1..... , <eos>).
item [b]
Its length is = 2 + [b[(++1). Define the index map for item j and level E:
u(j = 1 + (j++(jja- (j-1)(L+1)+ +1, We then specify exactly two sets:
u(j, =(j,)==(jj)) u(j.0) +,, EE (1....,, L}.
(11)
Pag (1, U { (u(j.)) 0) 1 Saxke {u(j.e) : j= bb), l 1,..... L.). (12)
By construction, 2mag 0 Qeoute = and Qaag U [U'] Positions in Qaag are never masked; corruption and prediction operate only Quode (including the dedup level f-
14

---

Published as a conference paper at ICLR 2026
Table 6: Dataset statistics. N is the catalog size (total number of items in the dataset); Marin/vallesst are the number of bundles in train/val/test sets.
Dataset
N
Munin
Myal
Mist
Spotify,
254,155
321,929
1.374
2,744
Spotify k660
254,155
253,358
798
1,582
Spotify k=90
254,155
188,618
463
969
POG 31,217
29,704
1,303
2,521
Algorithm RVQ-ENCCOE for item embedding
Require: Item embedding E() R semantic codebooks ( c(..))) with C(
C2 -e(
Jc C IR
dedup indexer Didup(i) [1, (1....; Ct)
Ensure: Code indices z(i) (2 s.,.) and reconstruction É(i)
1: r + E(t); F. t 04
2: for f = 1 to L - 1 do
D semantic levels (tie-break: smallest index)
3: 24, argmin
|| 2
cE(I...,ct) Cc}
4: É É + e
r r e
(2)
5: end for
6: zg,t. Didup(1)
non-semantic dedup level
7:
return z(i), B(i) E
RVQ encoding pseudocode. We elucidate the pscudocode in Algorithm specifyynng the encoding for an item embedding.
Evaluation metric setting. To quantify the latent-space alignment between the predicted playlist Prredict and the target playlist Prargets we define the Optimal Aligument Similarity (OAS). Specifically, for each track 4 E PTagget and ig E PPrediet- we compute a pairwise similarity score S(,, (4) based on their item embeddings. This induces weighted bipartite graph, where the two node sets correspond to tracks in PTarge and PPrediet. respectively, and each edge is weighted by the corresponding similarity score.
We then seek the optimal bipartite matching that maximizes the total similarity:
P
arg max
Σ
(13)
(LEEE
where P is valid matching between tracks PTange and PPredict- Based on the optimal matching P*, we define OAS as
OAS AAS(prredict PTagee)
Σ
S(1, 1z).
(14)
PPaagett
(K.G)))
Intuitively, OAS measures how well the predicted playlist aligns with the target playlist in the latent space, even when the exact track identities do not match. higher OAS indicates better semantic alignment and better prediction quality.
Hungarian algorithm. We compute the optimal matching P using the Hungarian algorithm. Since the Hungarian algorithm solves minimum-cost assignment problem, we convert pairwise similari- ties into costs via 1 S(t,, fy). solve the corresponding assignment, and then convert the result back into a similarity- based score. The detailed procedure is shown in Algorithm
C ADDITIONAL RESULTS
Comparison across datasets using Jaccard. We compare the results across datasets using Jaccard with multiple attempts. As Table shows, among the established baselines, BundleNAT generally achieves the best Jaccard performance across the Spotify datasets. This suggests that BundleNAT's
15

---

Published as a conference paper at ICLR 2026
Algorithm 2 Constraint-awarr order-agnostic decoding (inference)
Require: Observed item set bx: index maps u(j, E) and INVIDx(u) (i. E): code-domain valid sets (v(0); diffusion model ps; horizon
Ensure: Clean token matrix () and completed bundle b
1: Initialize with tokens for Qs and Aagi set 2u. +- [MASK] for all a Qy
2: while there exists a E S2 with Zn = [MASK] do
[L,.... T) (e.g., t= t= TT--s s at step or by schedule) 4: for all 2, with Zu [MASK] do
3: Choose timestep
(), (u)
6: π - (- ( =
categorical over {1,..., Cet (no [MASK]]
7:
mask out invalids: T[c] + 0 for e vie); a at a /.t/E... F(d
8: P(u) <
end for
Select reveal set S {u Oy Zu = [MASK]] (e.g,, top-k by max P(u), lowest-entropy, or reveal ratio 1)
11:
for all u E do
12:
decode: Zu <- arg max P(u) (or sample with temperature/op-p))
13:
clamp: 2u stays unmasked thereafter
14:
end for
15: end while
16: Z <- Z
17: return (
b via is (2211))) for all
von-auto-regressive architecture is particularly effective at generating relevant set-based results com- pared to the sequential models. What's s more, proposed method, DDBC, consistently and sig- nificantly outperforms all baselines across every dataset and attempt level. On Spotify the DDBC model achieves Jaccard of 0. 0.164, nearly doubling the performance of the best baseline (BundleNAT at 0.090). This performance gap confirms the efficacy and advanced capability of our model, especially when generating predictions with multiple attempts.
Table 7: Comparison across datasets using Jaccard with A E {1,5, 20}. Best in bold, second best underlined.
Model (A/bcam)
Spotify
Spotify
Spatify
POG
Jace@1 1
Jacc
Jace 20
Jacc
Jacc@8
Jace@220
Jacc@
Jace
Jacc 20
Jacc
Jacc
Jane @0
CLII
.009
.005
.002
.008
.004
.002
.007
.003
.001
.059
.048
.020
.023
.14
.024
TIGER
.053
028
0011
076
.036
.013
070
.034
.013
.157
.094
.038
BundleNAT
090
076
003
.056
055
.07
.052
.022
026
.097
.055
.033
DUBC
.055
.132
032
Latent-space quality. To better explore the latent-space quality of the items generated by our method, we report the OAS metric at A 50, shown in Table g For the Spotify dataset ries, when the bundle length (k) increases from 30 to 90, the latent-space quality becomes more stable. Specifically, the average OAS increases consistently from 0.603 (Spotify^=30) (Spotify==0o) and finally to 0.685 (Spotify*=so). Since higher OAS indicates higher similarity (better alignment) in the latent space, this trend suggests that our method has an improved capacity to model longer bundles.
0.662
Additional ablation study results. We report ablation study results on Spotify (A=l or A=10) in Table The results obtained at A=10 are consistent with those observed at A=1. (1) The Residual Vector Quantization (RVQ) component exhibits be absolutely indispensable. This result confirms the substantial mechanism of RVQ to mitigate the dimensionality curse caused by the huge item cat- alog size (N). (2) The boi token could provide positional guidance and improve latent space quality largely. Removing the boi token results in significant performance degradation. (3) Simple data augmentation (item swapping) proves to be beneficial technique for enhancing order-agnostic mod- eling and improving model robustness by mitigating overfitting specific bundle arrangements. (4) Although the Token Validity Filter yields only marginal performance improvement, its inclusion remains necessary to guarantee the validity of the generated bundles during inference.
16

---

Published as a conference paper at ICLR 2026
Algorithm 3 OAS via Hungarian Algorithm (maximize sum of cosine similarities)
Require: Predicted set by = (,,,...;AA)
3n (duplicates removed); ground-truth set by ffi..... in embed-
dings E(-)
Ensure: Optimal matching P C [l....,ff fi) x (L...., .1) and OAS
1: build similarity: S E _2ax= with S(a, bj +- {
2: + max(fi, v))
3: build square cost: Rm
Di convert max- maxx-iiillarity to min-cost
4: for a a== to m do
5: for b = 1 to do
6: a < ń and
then Cla, bj <- S(a, bj
cost [0. 2] since cos E [[1, 1]
8:
else
10: end Cla, b] x-
9:
dummy pairs have similarity 0
end for 12: end for
13: row reduction: Ō|a. f- .] miny Cla bj for all
column reduction: C|: b] <- C|, min, Cla, b]
15: repeat
16: Cover all zeros in Ö by the minimum number of borizontal/vertical lines
17:
if (#lines < m) then
18:
4- min [C'aa b] Ö(a, bj is uncovered) Subtract A from every uncovered entry Add A every doubly-covered entry (singly-covered entries unchanged)
19:
20:
21:
22:
end if
23:
until #lines = m
24:
extract assignment: find m independent zeros (no two share row/column) to form an optimal assignment
PC PC (l....,m}²
25: restrict real items: P ((a,b) E P:a a bsn]
26: Sum + "(aMEE Sla,b)
27: OAS Sam
higher is better
28: return P. .AS
Table 8: Latent-space quality A 50 measured by OAS1. We report (min, avg, max, var) of OAS over test bundles.
Dataset
min
avg
max
var
Spotify
0.477
0.603 0.717 0.003
Spotify ko
0.582
0.662 0.733
0.001
Spotify 90
0.625
0.685
0.738 0.001
POG
0.246
0.525
0.791
0.018
C.I EFFECT OF DIFFUSION STEPS
We further study how the number of reverse diffusion steps T affects performance. All results are reported on Spotifyx=30 under the default evaluation protocol with A = 1. As shown in Table I0] increasing consistently improves performance from very small values, but the gain quickly satu- rates beyond moderate range. Based this trade-off between effectiveness and efficiency, 25 in the main experiments.
The results confirm intuitive trend: too few denoising steps under-utilize the diffusion process, while excessively large T yields only marginal improvements. This supports our choice of a moder- ate default horizon in the main paper.
17

---

Published as a conference paper at ICLR 2026
Table Ablation study on Spotify==>> 30 (A=l vs, A=10). "Proposed" is our model DDBC; each of the other variants changes exactly one component that is removed from the proposed method.
A=1
A=10
Variant
Fl f
Jace
OAS
Jace f OAS f
Our proposed DDBC
0.282
0.177
0,660
0.166
0.092
0.620
w/o RVQ
0.021
0.011
0.557
0.028
0.015
0,556
w/o token validity filter
0.276
0.173
0.163
0.090
w/o boi token
0.176
0,104
0.538
0.116
0,063
0.536
w/o data augmentation
0.254
0.158
0.599
0.152
0.084
0.598
Table 10: Effect of diffusion steps T on Spotifyk=30
F1 f
Jaccard
OAS t
0.2693
0.1656
0.6578
0.2713
0.1673
0.6571
0.2783
0.1724
0.6595
10
0.2798
0.1729
0.6604
0.2821
0.1753
0.6604
25
0.2821
0.1756
0.6600
32
0.2851
0.1771
0.6616
50
0.2850
0.1771
0.6618
0.2845
0.1773
0.6618
100
0.2832
0.1759
0.6595
200
0.2815
0.1745
0.6604
300
0.2816
0.1749
0.6601
C.2 ROBUSTNESS TO THE CHOICE OF OBSERVED ITEMS
In the main experiments, we use the front part of bundle as the observed subset b which ensures a fair comparison with sequential baselines trained under a left-to-right objective. To test whether DDBC is sensitive this choice, additionally evaluate three selection strategies for the observed items: Prefix (the first half of the bundle), Suffix (the second half), and Random (a random 50% subset).
Table I1 shows that DDBC remains highly stable across all three settings, with only minor variations in F1, Jaccard, and OAS. This suggests that the model is not strongly tied to a particular observed- item ordering and is robust to different purtial-bundle configurations.
The differences are small (AFI < 0.004 and AJaccard S 0.003), indicating that DDBC largely insensitive to which half of the bundle is observed. Minor fluctuations are still plausible, as some bundles may contain weak local sequential regularities.
C.3 TRAINING-FREE VARIABLE- LENGTTH GENERATION
Although the main paper focuses on a fixed-length evaluation protocol, DDBC can be adapted to variable-length generation without retraining. In this subsection, we report three simple inference- time strategies on Spotify:=30 using the same trained model.
Direct variable-length decoding. We first directly change the number of item slots to be predicted from the fixed training length to a new target length bs. The results Table 12 show that the model maintains competitive performance across reasonably wide range of target lengths. In particular, when bs is close to the training length, the degradation is negligible.
Semi-AR blockwise decoding. Inspired by blockwise generation, we also consider simple semi- autoregressive (Semi-AR) strategy. At each pass, the model predicts bs new items conditioned on the observed bundle b and the items generated so far; this process is repeated for R passes. Table T3
18

---

Published as a conference paper at ICLR 2026
Table 11: Impact of observed-item selection strategy on Spotify k=0 (A
Strategy
F1
Jaccard f
OAS
Prefix
0.2821
0.1756
0.6600
Suffix
0.2777
0.1717
0,6575
Random
0.2791
0.1727
0.6587
Table 12: Direct variable-length generation on Spotifyx=30 without retraining.
Target length bs
Recall f
Precision t
F1 1
Jaccard f
15
0. 1550
0.3099
0.2066
0.1212
20
0.2002
0,3003
0.2403
0.1449
25
0.2004
0.3006
0.2405
0.1449
30
0.2821
0,2821
0.2821
0.1756
35
0.2415
0.2898
0,2635
0.1613
40
0.3878
0.2585
0.3102
0.1950
45
0.3868
0.2579
0.3094
0.1942
shows that, as long as the per-pass block size is not too small, the performance remains close the default fixed-length setting.
Multi-sampling with set merging. Finally, test a non-Semi-AR alternative: draw multiple completions, merge the generated items into a candidate set, and evaluate the merged result against the target bundle. As shown in Table [4] this strategy leads similar conclusions and often effective when moderate over-genede wer-generatiion is allowed.
note on block size. We observe that using moderate block size (roughly bs E [5, 10) can yield slightly better performance than predicting the entire bundle in a single shot. We conjecture that this may because a bundle can contain multiple sub-themes, and generating items in several paced rounds may encourage covering different sub-themes across rounds rather than collapsing onto single dominant mode. This hypothesis preliminary, and we leave a more principled analysis to future work; it may also have implications for sequential recommendation. where multi-interest structure commonly observed.
Overall, these preliminary results suggest that DDBC is not inherently tied to single fixed output length. Even though the model is trained under a fixed-length protocol, it can still support variable- length generation through lightweight inference-time modifications, without any retraining. A more principled treatment stopping criteria and length control remains an important direction for future work.
D FURTHER DISCUSSION
D.1 FROM-SCRATCH BUNDLE GENERATION
Although our main evaluation follows the standard partial-to-full completion protocol, DDBC also defines an unconditional bundle prior and can generate bundles from scratch by initializing all item- code positions in Qcote as [MASK] (i.c.. b = 0 and running the same constraint- decoding in Algorithm This capability is naturally supported by our absorbing- learss to recover clean tokens from heavily corrupted states and thus exposes the denoiser to near- unconditional inputs; practice, all-mask samples tend to reflect global co-occurrence structure (frequent compatibilities are more likely to be generated jointly) and exhibit approximate order- insensitivity due to symmetric corruption. That said, without explicit conditioning, from-scratch sampling may drift toward popular generic bundles. and variable-length generation still lacks prin- cipled stopping/length control; while token validity guarantees catalog validity, it does not guarantee user-specific relevance, motivating personalization and length-control extensions future work.
diffusion training. which
19

---

Published as a conference paper at ICLR 2026
Semi-AR variable-length generation on Spotifye=30 without retraining.
Table 13:
Table 14: Multi-sampling variable-length gener-
ation on Spotify without retraining.
bs
Fl
Jaccard 1
R
bs
Jaccard f
30
0.1244
0.0689
30
1
0.1857
0.1101
0.2133
0.1261
0.1871
0.1111
0.2656
0,1632
10
3
0.2700
0.1687
6
0.2772
0.1716
6
5
0.2837
0.1755
10
0.2837
0.1761
5
6
0.2848
0.1768
15
0.2825
0.1755
10
0.2871
0.1782
0,2821
0.1756
0.2851
0.1770
30
0.2821
0.1756
D.2 PERSONALIZED BUNDLE GENERATION
Our current instantiation focuses on unconditional completion with personalization primarily mediated by frozen encoders for user-item signals and item semantics. In real deployments, however, bundle generation is rarely signal-free: systems typically have intent cues (e.g.. theme/genre//ategorr)) and user-specific preference signals, and the generated bundle should align with them. A lightweight, training-fre free way to incorporate such signals is (i) seed-then seed-then-complete:: use an existing user-conditioned recommender (similarity, rules/filters, or profile-based recall) to re- trieve a small set of seed items and then let DDBC expand it into a coherent full bundle; and (ii) logit bias / external guidance: during denoising, add bias from an external user-conditioned score (e.g., user embedding similarity category priors) to steer sampling while keeping the token- ooken-validity constraints. A more principled direction to make the diffusion process explicitly conditional (c.g., injecting user/context features into the denoiser and training under the same masked objective), which could better trade off relevance, diversity, and controllability under personalization.
D.3 CANDIDATE-POOT EVALUATION: RATIONALE AND LIMITATIONS
We evaluate under a controlled candidate pool rather than over the full item universe, and this choice is motivated by three pragmatic considerations. First, it ensures fair comparability: many strong baselines in bundle constuection/eccomnnnatioo are inherently candidate-conditionel (e.g., retrieval-then-rank or candidate-scorin pipelines), so removing the candidate pool would make comparisons ill-defined or require ad-hoe changes that alter computational budgets and failure modes. Second, it partially addresses a real-world non-uniqueness issue: bundle construction often admits multiple valid solutions, and logged ground- -rutt bundles typically reflect only one feasible realization among many; near-neighbor substitutions (items that semantically interchangeable) may yield equally coherent bundles yet be absent from the collected data, a recurring evaluation challenge in recommender systems beyond bundling. Third, it improves statistical reliability: in the fully open-world setting, exact-match hit rates can become extremely small for all methods, making results dominated by random variation and undermining meaningful comparisons; restricting shared candidate pool keeps success probabilities in measurable range and reduces variance. We view this protocol as reproducible compromise for benchmarking, while recognizing does not fully capture open-world solution diversity; developing evaluation procedures that better credit mul- tiple valid completions (e.g., graded relevance or set-level equivalence) remains important future work.
20


Reviews:
[{"review_id": "F8vR61j4Mz", "reviewer": "Reviewer_UnGS", "summary": "This paper proposes a discrete diffusion based bundle construction method. To address the complexity challenge of bundle construction caused by the bundle size and large item corpus, it (1) uses RVQ to get the code representation of each item by training a shared codebook; and (2) trains a discrete diffusion model to gradually mask items in a given bundle in the forward process and then gradually reconstruct the masked items in the reverse process with the item token learned through RVQ module. Experiments on two real-world dataset partially prove the effectiveness of the proposed method (as from the result, the proposed method only works well on one of the adopted dataset with larger bundle size). Overall, this is a quite solid study on bundle construction.", "questions": "Q1. How to distinguish the tokens of unpopular items using RVQ? Existing study shows that RVQ in the Euclidean space may not be able to well distinguish the unpopular items, which has a large amount in the real-world scenarios. \n\nQ2. Does the step T affect the performance? If so, how?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "S1. The paper is generally well written and organized, which makes it easy to follow. \n\nS2. The investigated research question is quite meaningful and practical in the real-world application. More importantly, the authors identified the limitations of the existing sequential-based bundle construction, as the order of the items within a bundle may not matter a lot when constructing the bundle (it could be a set).\n\nS3. The effectiveness of the model has been verified on the Spotify dataset with the large bundle size, while it does not work on the POG dataset with smaller bundle size. \n\nS4. Extensive ablation studies and important hyper-parameter analysis further show the efficacy of the important modules of the model\n\nS5. The source code is provided to ensure a better reproducibility.", "weaknesses": "W1. The title does not really reflect the task that has been investigated in the paper. The paper actually investigates the bundle completion task instead of exact bundle construction task. \n\nW2. It would better if the authors can highlight their technical contribution. \n\nW3. The investigate the research question, though being practical and meaningful in real-world application, seems to lack generalizability. It relies on partial items in a bundle, so cannot create a bundle from scratch. However, in the real-world applications, there are many scenarios, where creating bundle from scratch is required. \n\nW4. Some related works are missing, for instance, Adaptive In-Context Learning with Large Language Models for Bundle Generation (SIGIR 2024). The authors are highly suggested to cover a comprehensive literature, especially LLM based method for bundle construction/completion. \n\nW5. The fixed-length setting may limit the flexibility of the proposed model. In the real-scenario, we may not be able to show too many items for the users in one page, so how to determine the subset of the items that should be displayed to the user?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zARI2evOuz", "reviewer": "Reviewer_B6yG", "summary": "The paper proposes DDBC, which is a discrete diffusion for bundle construction. The core motivation is that pervious bundle construction methods are based on sequential generation, where bundle length grows results in intra-bundle relational explosion and large catalog size makes item search space massive. DDBC treats bundle construction as masked discrete denoising over a compact discrete code space. DDBC quantizes item embeddings via multi-level RVQ, running masked discrete diffusion over the codes, and decoding the codes back to item IDs. The experiments show significant gains (about 100%) on some of the baselines.", "questions": "Could the diffusion be modified to support variable-length bundle reconstruction?\n\nCould DDBC extended to personalization scenarios? e.g., change architecture to conditional diffusion and inject the user preference using the conditions.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The bundles are regarded as sets not sequences, which is . And the combination of the masked discrete diffusion and RVQ for bundle generation is novel in this domain.\n\nThe improvements are significant compared to the baselines. DDBC achieves >100% relative gains in Jaccard and F1 on Spotify with k = 60/90. DDBC scales well to have bigger relative improvements on the datasets with larger k.\n\nDDBC is tiny and cost less inference time compared to many baselines like BundleMLLM.", "weaknesses": "The size of bundle seems to be fixed-length. If so, the application of DDBC could be limited. DDBC does not model set invariance. Although the bundles are not designed as serialized sequences and order is randomized, permutation invariance is not considered.\n\nThe evaluation includes only playlist and POG. I wonder if DDBC still performs well when bundles are from completely different domain, e.g., shopping sets from different categories.\n\nThe way of handling personalization is not explored. The generation is unconditional w.r.t user preferences, e.g., the RVQ codebooks of DDBC are global, potentially flattening user preference patterns. The current framework may hardly be deployed to scenarios where personalization is required.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "t3Tjhqe3Lh", "reviewer": "Reviewer_ZPfg", "summary": "In this paper, the authors propose DDBC (Discrete Diffusion for Bundle Construction), a novel framework that formulates bundle construction as a masked discrete diffusion process. Rather than following traditional step-by-step methods, DDBC generates bundles in an order-independent way by progressively filling in masked item tokens. The framework combines Residual Vector Quantization (RVQ), which represents items with discrete semantic codes to address the challenge of large item catalogs, with a Discrete Diffusion Model (DDM) designed to capture complex relationships within bundles without requiring a fixed item order. Comprehensive experiments on Spotify playlist and fashion outfit datasets show that DDBC achieves substantial performance improvements over both sequential and set-based baselines. Ablation studies further highlight the complementary strengths of RVQ and the discrete diffusion backbone.", "questions": "1. At $t=T$, all tokens are fully masked, yet the model is trained to predict original tokens under Equation 7. While this teaches the model unconditional bundle priors, could the authors clarify: \n    - a) What proportion of training loss comes from high-noise timesteps ($t \\geq 0.8T$)\n    - b) Whether this supervision is necessary given that inference always starts from partially-observed bundles\n    - c) Whether alternative training strategies (e.g., restricting $t < T$) were explored?\n2. During inference, how are the “known” items in $b_x$ selected? Since bundle semantics could vary depending on which subset is revealed, does the model show robustness to different partial-item configurations?\n3. When bundles exceed the capped size $k$, how are items selected for truncation? Does this selection (e.g., first-k, random-k, most-popular-k) introduce bias toward specific bundle patterns? Have the authors analyzed whether truncation affects semantic coherence or diversity of the resulting training data?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 1, "strengths": "1. The paper presents a well-motivated argument against the sequential construction paradigm, emphasizing that bundles are inherently unordered sets rather than sequences.\n2. The integration of discrete diffusion and residual vector quantization is technically coherent and aligns with recent advances in generative recommendation.\n3. The paper provides extensive experiments with clear ablations and sensitivity analyses, showing that DDBC scales better with longer bundles and larger catalogs.", "weaknesses": "1. While the paper demonstrates robustness across different input-predict ratios, the framework fundamentally requires at least some partial bundle items at inference. The paper does not explore conditional generation from fully-masked states using only user embeddings or contextual features, which limits applicability for cold-start scenarios where no seed items are available.\n2. The model enforces a fixed number of items per bundle, whereas real-world bundles are inherently variable in size. Capping bundle lengths during training and testing introduces a methodological limitation that does not fully capture the characteristics of the bundle item collection as in original dataset.\n3. While the integration of RVQ with discrete diffusion is technically sound and well-executed, the core novelty lies primarily in combining existing techniques (RVQ from generative retrieval and masked diffusion from language models) rather than introducing fundamentally new algorithms. The ablation study demonstrates that both components are essential and complementary, but the contribution is more engineering-focused than conceptually novel. The paper would benefit from deeper theoretical analysis of why this combination works particularly well for bundle construction.\n\nMinor typos:\n-\tL122: Citation formatting error\n-\tL196: Use $z_{j,l}$ instead of $z_{jl}$\n-\tL244: The reverse process should be conditioned on current noisy tokens $Z^{(t)}$\n-\tL267: $\\hat{E}_j = \\sum_{l=1}^{L-1} e^{(l)}_{z^{(l)}(i)}$\n-\tL235, L287: The notation $\\alpha(t) != \\alpha_t$; $\\alpha(t)$ should be $1-t/T$ to yield deterministic at $t=T$", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "51SK1d3rtd", "reviewer": "Reviewer_CnC2", "summary": "Bundle construction suffers from a massive item pool and exponentially growing combinations. \nDDBC addresses these challenges by utilizing a diffusion model to generate an entire bundle. \nDDBC also quantizes item embeddings into discrete codes to reduce the search space.\nExtensive experiments show that DDBC outperforms current bundle generation methods and achieves the state-of-the-art performance.", "questions": "* How does a STE work for a codebook quantization?\n* How does the RVQ strategy illustrate an item in coarse-to-fine manner?\nSharing the same codebook for all positions without scaling seems to treat all tokens equally rather than hierarchically.\n* Even if each item is quantized into a unique code sequence, it seems permutations of the sequence would represent semantically same features since dequantizing the residual quantization is aggregating all codes of the sequence.\nHow does this affect the diffusion process?\nIs there a way to utilize this during the diffusion process?\n* How does the dedup code working? Does it included in the codebook? Should the diffusion model recover the dedup code by denoising?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "* Tokenizing items through codebook quantization is effective for processing a massive item pool.\n* DDBC outperforms existing baselines by a huge margin.", "weaknesses": "* The size of bundle is fixed and not adjustable, unlike other baselines.\n* Using the same item features for all baselines is doubtful. Each model may require its own embedding space depending on its architecture.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)