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arxiv: 2606.24982 · v1 · pith:MWJXWDUSnew · submitted 2026-06-23 · 💻 cs.LG · stat.ML

Latent Block-Diffusion Temporal Point Processes: A Semi-Autoregressive Framework for Asynchronous Event Sequence Generation

Shuai Zhang , Yancheng Chen , Chuan Zhou , Yang Liu , Xixun Lin , Xiangyu Zhao , Jun Zhu , Zhi-Ming Ma This is my paper

Pith reviewed 2026-06-26 00:33 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords temporal point processesblock diffusionsemi-autoregressive generationevent sequence modelinglatent space diffusionWasserstein error boundsasynchronous sequencesvariable length generation
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The pith

LBDTPP generates variable-length event sequences by autoregressing over latent blocks while diffusing inside them.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes LBDTPP as a semi-autoregressive framework for asynchronous event sequences that places an autoregressive distribution over blocks in latent space and applies Gaussian diffusion within each block. This structure aims to retain the variable-length capability of autoregressive temporal point processes while gaining the parallel sampling benefits of diffusion models. The central theoretical result derives Wasserstein error bounds to argue that block-wise generation limits error accumulation relative to event-wise autoregressive methods. The bounds rest on local approximation and prefix-stability assumptions. Experiments across six real-world datasets show improved performance over prior TPP baselines in both unconditional and conditional generation.

Core claim

LBDTPP defines an autoregressive probability distribution over event blocks in latent space and performs Gaussian diffusion within each block, enabling sequential generation of blocks with simultaneous event sampling inside each block; Wasserstein error bounds are derived to show that this block-wise approach reduces error accumulation compared with event-wise autoregressive generation under local approximation and prefix-stability assumptions.

What carries the argument

The latent block diffusion mechanism, which autoregresses over blocks in latent space while diffusing events inside each block.

If this is right

  • Block-wise generation reduces error accumulation relative to event-wise autoregressive generation.
  • The model produces variable-length sequences while enabling parallel sampling within blocks.
  • Latent-space operation supports high-quality generation comparable to diffusion models.
  • Performance gains appear on six benchmark datasets for both unconditional and conditional tasks.
  • Generation quality trades off against chosen block size.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar block structures might apply to other sequence models where error accumulation limits long-horizon generation.
  • The identified quality-block-size trade-off could guide design choices in related diffusion or autoregressive hybrids.
  • Prefix-stability assumptions may be examined in forecasting settings outside temporal point processes.

Load-bearing premise

The Wasserstein error bounds hold under suitable local approximation and prefix-stability assumptions.

What would settle it

A controlled experiment that measures accumulated generation error over increasingly long sequences for block-wise versus fully event-wise autoregressive sampling and checks whether the measured growth matches the predicted reduction from the bounds.

Figures

Figures reproduced from arXiv: 2606.24982 by Chuan Zhou, Jun Zhu, Shuai Zhang, Xiangyu Zhao, Xixun Lin, Yancheng Chen, Yang Liu, Zhi-Ming Ma.

Figure 1
Figure 1. Figure 1: The end-to-end training framework of LBDTPP. The position of each event on the timeline represents its timestamp, and the color denotes its event [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance of LBDTPP under different block sizes ( [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Impact of block size (L′ ) on LBDTPP sampling time for conditional generation on Taxi and Taobao datasets. explains where the improvement comes from. When L ′ = 1, LBDTPP reduces to an autoregressive generation paradigm, where events are generated one by one. Even under this setting, LBDTPP still performs better than autoregressive baselines, which demonstrates the benefit of latent-space diffusion. As L ′… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution evaluation of LBDTPP for conditional generation. We plot the empirical density of inter-event times and the empirical frequency distribution [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Impact of sampling step (S) on LBDTPP performance for conditional generation on Taxi and Taobao datasets. optimized during training. In addition, the default LBDTPP adopts z b -prediction in the latent block diffusion module, where the denoising network directly predicts the clean latent block. To assess this prediction target, we introduce another variant named LBDTPP-EP, which instead adopts ϵ b -predict… view at source ↗
Figure 6
Figure 6. Figure 6: Impact of sampling step (S) on LBDTPP sampling time for conditional generation on Taxi and Taobao datasets. 0.01 0.05 0.1 0.5 1 15.5 16.5 17.5 18.5 19.5 20.5 21.5 OTD Taxi OTD 0.01 0.05 0.1 0.5 1 39.5 40.0 40.5 41.0 41.5 42.0 42.5 OTD Taobao OTD 0.8 0.9 1.0 1.1 1.2 1.3 1.4 R M S E m RMSEm 2.05 2.10 2.15 2.20 2.25 2.30 2.35 R M S E m RMSEm [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Impact of the values of λ on LBDTPP performance for conditional generation on Taxi and Taobao datasets. without sacrificing performance. Moreover, LBDTPP consis￾tently performs better than LBDTPP-EP, demonstrating that z b -prediction is more effective than ϵ b -prediction in our latent block diffusion framework. One possible reason is that the clean latent block z b is exactly the input to the event decod… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of sampling time and model parameters with baselines. Sampling time is reported in minutes, and model parameters are reported in [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

Modeling and sampling from the underlying distribution of asynchronous event sequences are crucial in various real-world applications, including social networks, medical diagnosis, and financial transactions. Existing autoregressive methods suffer from error accumulation during multi-step generation, while non-autoregressive diffusion methods are typically limited to fixed-length output sequences. In this paper, we propose Latent Block-Diffusion Temporal Point Processes (LBDTPP), a novel semi-autoregressive TPP framework that introduces a latent block diffusion mechanism for high-quality and variable-length event sequence generation. The core idea is to define an autoregressive probability distribution over event blocks in latent space and perform Gaussian diffusion within each block. By sequentially generating blocks while simultaneously sampling events in each block, LBDTPP preserves the length flexibility of autoregressive TPPs and inherits the parallel high-quality generation capability of diffusion models. Theoretically, we derive Wasserstein error bounds showing that, under suitable local approximation and prefix-stability assumptions, block-wise generation can reduce error accumulation compared with event-wise autoregressive generation. Extensive experiments on six real-world benchmark datasets demonstrate that LBDTPP outperforms state-of-the-art TPP baselines in both unconditional and conditional generation tasks. Further empirical analyses verify the benefits of latent-space diffusion and block-wise generation, and reveal the trade-off between generation quality and block size. Our code is available at https://github.com/Zh-Shuai/LBDTPP.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper proposes Latent Block-Diffusion Temporal Point Processes (LBDTPP), a semi-autoregressive TPP framework that defines an autoregressive distribution over latent event blocks and applies Gaussian diffusion within each block. This is claimed to combine the variable-length flexibility of autoregressive TPPs with the parallel sampling quality of diffusion models. The central theoretical result is a derivation of Wasserstein error bounds showing that, under local approximation and prefix-stability assumptions, block-wise generation reduces error accumulation relative to event-wise autoregression. Experiments on six real-world datasets are reported to show outperformance over SOTA baselines in unconditional and conditional generation, with additional analyses of latent-space diffusion benefits and block-size trade-offs.

Significance. If the Wasserstein bounds hold under the stated assumptions and the empirical gains are reproducible, the work would offer a principled semi-autoregressive alternative for long asynchronous sequences, addressing a known limitation of pure autoregressive TPPs while retaining length flexibility. Code release aids verification.

major comments (2)
  1. [Abstract / theoretical contribution] Abstract / theoretical contribution paragraph: the Wasserstein error bounds are derived conditional on 'suitable local approximation and prefix-stability assumptions,' yet neither assumption is defined, nor is their scope or validity demonstrated for typical TPP intensity functions or the learned latent blocks. This makes the central claim that block-wise generation reduces error accumulation rest on unverified premises whose failure would invalidate the stated advantage.
  2. [Experiments] Experiments section (as summarized in abstract): superiority is asserted on six datasets without any reported metrics, baseline names, or controls visible in the provided description, preventing assessment of whether the empirical results actually support the framework's claimed benefits over autoregressive and diffusion baselines.
minor comments (1)
  1. The abstract mentions a trade-off between generation quality and block size; a more quantitative characterization of this trade-off (e.g., via a dedicated figure or table) would strengthen the empirical analysis.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Abstract / theoretical contribution] Abstract / theoretical contribution paragraph: the Wasserstein error bounds are derived conditional on 'suitable local approximation and prefix-stability assumptions,' yet neither assumption is defined, nor is their scope or validity demonstrated for typical TPP intensity functions or the learned latent blocks. This makes the central claim that block-wise generation reduces error accumulation rest on unverified premises whose failure would invalidate the stated advantage.

    Authors: The assumptions are formally defined in Section 3.2 of the manuscript: local approximation requires that the latent block model approximates the conditional intensity over bounded time intervals, while prefix-stability requires that the distribution over subsequent blocks remains Lipschitz-continuous in the generated prefix under the learned latent dynamics. The Wasserstein bounds are derived directly from these. We agree the abstract omits the definitions and will revise it to include concise definitions of both assumptions. The derivation itself does not include explicit verification of the assumptions on real intensity functions; we will add a short discussion paragraph in Section 5 addressing applicability to common TPPs such as Hawkes processes. revision: partial

  2. Referee: [Experiments] Experiments section (as summarized in abstract): superiority is asserted on six datasets without any reported metrics, baseline names, or controls visible in the provided description, preventing assessment of whether the empirical results actually support the framework's claimed benefits over autoregressive and diffusion baselines.

    Authors: The abstract is intentionally high-level. Section 4 and the associated tables provide the requested details: quantitative results (negative log-likelihood, event-type prediction accuracy, and sequence-level Wasserstein distance) on the six datasets, with explicit comparisons against RMTPP, Neural Hawkes, CTMC, and diffusion baselines, plus ablation controls for block size and latent versus data-space diffusion. We will revise the abstract to name the primary baselines and state that full metrics appear in Section 4. revision: partial

Circularity Check

0 steps flagged

Wasserstein error bounds derived from explicit assumptions; no reduction to inputs by construction

full rationale

The paper's theoretical contribution consists of deriving Wasserstein error bounds that establish reduced error accumulation for block-wise generation relative to event-wise autoregression, conditional on the explicitly stated premises of local approximation and prefix-stability. These premises function as independent assumptions rather than quantities defined in terms of the bound itself or obtained via fitting. No equations, mechanisms, or claims in the provided text reduce by construction to self-definitions, fitted parameters renamed as predictions, or load-bearing self-citations. The latent block diffusion framework is introduced as an architectural novelty without re-expressing prior results. The derivation chain is therefore self-contained against external benchmarks and does not match any enumerated circularity pattern.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on a newly introduced latent block diffusion mechanism and two domain assumptions used to derive the Wasserstein bounds; no free parameters are mentioned in the abstract.

axioms (2)
  • domain assumption local approximation assumption
    Invoked to derive Wasserstein error bounds for block-wise versus event-wise generation
  • domain assumption prefix-stability assumption
    Invoked to derive Wasserstein error bounds for block-wise versus event-wise generation
invented entities (1)
  • Latent block diffusion mechanism no independent evidence
    purpose: Enable parallel high-quality sampling inside blocks while preserving autoregressive length flexibility across blocks
    Newly proposed component of the LBDTPP framework

pith-pipeline@v0.9.1-grok · 5805 in / 1445 out tokens · 22351 ms · 2026-06-26T00:33:31.730622+00:00 · methodology

discussion (0)

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