REVIEW 5 major objections 5 minor 24 references
ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes
T0 review · 5 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash
Pith's one-line read This paper claims that temporal point processes are best modeled by diffusion schedules that corrupt later events first, so generation reconstructs the past before forecasting the future, and it derives the flow-matching objective that…
desk verdict A useful asynchronous flow-matching recipe for TPP long-horizon forecasting, held back by an unproven conditioning step and a missing key baseline. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the matrix-valued asynchronous noise schedule $A(s) \in \mathbb{R}^{N\times N}$: a diagonal matrix whose $i$-th entry is the fraction of event $i$'s latent representation still present at flow time $s$. The paper chooses a piecewise-linear ramp (Eqs. 6–7) that staggers the noise arrival times $(N-i)/(2N-1)$ and completion times $(2N-i)/(2N-1)$ across events, so the most recent event is fully corrupted first and the earliest event last, inverting that order in generation time. This single object does three jobs: it defines the data-to-noise interpolation, it defines the generation ODE through its derivative $A'(s)$, and its diagonal staggering implements the inductive bias that a clean past conditions the future. The argument's second pillar is the identity $A'(s)A(s)^\dagger A(s) = A'(s)$ proved in Proposition A.4 by treating $d/ds[A(s)^\dagger A(s)]$ as a sum of Dirac deltas at the moments each event becomes pure noise; this is what lets the model regress $x_0 - \epsilon$ directly rather than the numerically ill-behaved $A'(s)A(s)^\dagger[x_s - \epsilon]$. Around these sit a $\beta$-VAE mapping each event's (duration, category) pair to a continuous latent vector, and a masked diffusion transformer that takes the matrix $A(s)$ in place of the usual scalar timestep.
What would settle it
Evaluate, at a crossing point $s = s^{(i)}_{\mathrm{end}}$ of Eqs. 6–7, the matrix $A'(s)A(s)^\dagger A(s) - A'(s)$ using the left-derivative convention of Remark 4.4 and the Moore–Penrose pseudo-inverse; any nonzero entry falsifies Proposition A.4 and means Eq. 16 trains the wrong vector field. A cleaner end-to-end check: train the identical architecture with the invertible $\sigma_{\min}$-regularized schedule of Appendix B at $\sigma_{\min} = 10^{-4}$ and compare the generated sequences with ADiff4TPP's; if the identity were failing, the two models' ODE trajectories would diverge near the earliest crossing point instead of converging as $\sigma_{\min} \to 0$.
Extended reading notes
Core claim
On the paper's own terms, the discovery is that asynchronous diffusion is a valid and superior generative formulation for event sequences. With the interpolation $x_s = A(s)x_0 + (I-A(s))\epsilon$ between a latent event sequence and Gaussian noise, and a diagonal matrix schedule $A(s) \in \mathbb{R}^{N\times N}$ whose $i$-th entry ramps linearly from 1 to 0 over $[s^{(i)}_{\mathrm{start}}, s^{(i)}_{\mathrm{end}}] = [(N-i)/(2N-1), (2N-i)/(2N-1)]$, later events are fully noised first and, in reverse time, restored last — so generation reconstructs the past before the future. The load-bearing methodological result is that the conditional vector field simplifies from $A'(s)A(s)^\dagger[x_s - \epsilon]$ to $A'(s)[x_0 - \epsilon]$ (Proposition A.4) even though $A(s)$ is not invertible and not differentiable at the breakpoints; this yields the training objective $\mathcal{L}_{\mathrm{CFM}}(\theta) = \mathbb{E}_{s,x_0,\epsilon}\|A'(s)[(x_0 - \epsilon) - v_\theta(x_s, A(s))]\|^2$ and the generation ODE $\dot{x}_s = A'(s)v_\theta(x_s, A(s))$ for any positive semi-definite, monotone, continuous matrix schedule with $A(0) = I$, $A(1) = \mathbf{0}$. Forecasting is then one ODE solve on a shortened interval $[s_{\mathrm{start}}, s_{\mathrm{end}}]$: observed events are driven to their encoded latents, future events are generated by the diffusion transformer, and the same solver covers both next-event and 30-step-ahead prediction. Empirically the paper reports state-of-the-art next-event time RMSE on all five datasets and lower optimal-transport distance than every baseline at horizons 5, 10, 20, and 30.
Load-bearing premise
Everything hinges on one matrix-calculus identity — the derivative of the noise schedule times the schedule's pseudo-inverse times the schedule itself must equal the derivative alone, even at the instants when an event becomes fully noisy — and that identity is only established by a short distributional argument, so if it fails at those instants the training objective is no longer the true generative flow.
Editorial extensions
If this is right
- One trained model handles both next-event and long-horizon forecasting by moving the start and end points of the generation ODE, so evaluation no longer requires autoregressively appending each predicted event and re-encoding the history.
- Long-horizon predictions are conditioned on a fully reconstructed near past, because the schedule finishes denoising early events while later events are still being generated; the reported optimal-transport gap to baselines widens with horizon (average 24.5% improvement at horizons 5–30).
- The derivation legitimizes any positive semi-definite, monotone, continuous matrix-valued schedule, so schedules other than the linear ramp can be designed within the same objective.
- The ablations show the benefit is specific: replacing the staggered schedule with synchronous (rectified-flow) or disjoint (autoregressive-style) diffusion worsens next-event metrics, and removing the attention mask over future events also hurts — consistent with the paper's hypothesis that noisy distant events pollute near-term predictions.
Reading between the lines
- The asynchronous schedule is effectively a continuous dial between autoregressive generation (disjoint schedule) and whole-sequence diffusion (synchronous schedule), and the paper only turns the dial to one position; tuning the per-event start and end times per dataset — for instance, spacing them by how strongly each event type influences successors — is a natural untested extension that the same
- If the ordering of denoising is what drives the gains, then reversing the schedule (diffusing early events first) should reduce or eliminate the advantage; that experiment would separate the conditioning benefit from any side effect of the new objective.
- Because observed events are reconstructed exactly during forecasting (the $y^{(i)} - \epsilon^{(i)}$ term of Eq. 10), the forecast error decomposes into VAE representation error plus diffusion error in the prediction window; this decomposition could be used to decide where to allocate model capacity — a use the paper does not discuss.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proposes ADiff4TPP, a latent diffusion model for temporal point processes (TPPs) that uses a matrix-valued asynchronous noise schedule. The method first trains a β-VAE to embed each event's duration and category into a continuous latent vector, and then trains a diffusion transformer with a conditional flow matching objective on the joint latent sequence. A piecewise-linear diagonal schedule A(s) diffuses later events faster than earlier ones, and forecasting is performed by solving an ODE in which observed events are denoised exactly while future events are generated by the learned vector field. Experiments on five benchmark datasets report next-event prediction RMSE and error rate, long-horizon prediction via optimal transport distance, and ablations over latent dimension, noise schedule, and masking.
Significance. If the claims are substantiated, the asynchronous schedule is a useful and flexible idea: it allows variable-length prediction windows, generates earlier events first to condition later ones, and the reported RMSE and long-horizon OTD gains over the included baselines are consistent across datasets. Strengths of the manuscript include the explicit derivation of a flow matching objective for matrix-valued schedules, the ablation study comparing asynchronous, synchronous, and disjoint schedules, and evaluation on five datasets for both next-event and long-horizon tasks. However, the empirical state-of-the-art claim for event-type prediction is contradicted by the paper's own Table 1, the closest flow-matching baseline (Event Flow) is missing from all experiments, and the conditional forecasting ODE in Eq. (10) lacks a correctness argument. These issues currently prevent the paper from being accepted in its present form.
major comments (5)
- [Abstract and §5.1, Table 1] The abstract and introduction claim 'state-of-the-art results in predicting both the next inter-event time and event type,' but Table 1 contradicts this for event-type prediction: on Amazon ADiff4TPP's error rate is 67.5% versus 64.9% for IFTTPP and 65.4% for THP, and on StackOverflow it is 61.3% versus 55.4% for AttNHP and 57.7% for SAHP; §5.1 itself concedes superiority on only three datasets. Please revise the claims to match the reported numbers.
- [§5, Experiments] Event Flow (Kerrigan et al., 2024) is described in §6 as a flow-matching TPP method that predicts future events through a single denoising process, yet it is absent from every experiment in §5. Because this is the closest comparable method to ADiff4TPP, the reported 'state-of-the-art' results in Table 1 and Figure 4 are not benchmarked against the most relevant baseline. Please add Event Flow to the next-event and long-horizon comparisons, or explicitly justify its exclusion.
- [§3.4, Eq. (10)] The forecasting ODE in Eq. (10) is introduced as 'simple and intuitive,' but the paper does not prove that solving it samples p(x_F | x0^O = y_O). The CFM objective in Eq. (16) trains vθ to approximate the marginal conditional expectation E[x0−ε | X_s=x_s]; during the integration interval of Eq. (10), the observed coordinates x_s^O are noisy observations A_O(s)y_O+(I−A_O(s))ε_O, so vθ sees a noisy version of y_O and its Bayes-optimal output averages over the posterior of y_O rather than using the fixed value y_O. Please provide a derivation that Eq. (10) is the correct conditional flow, or explicitly characterize it as an inpainting heuristic and validate that choice against a proper conditional training objective or classifier-free guidance.
- [Appendix A.3, Proposition A.4] Proposition A.4 proves the key identity A′(s)A(s)†A(s)=A′(s) by treating d/ds[A(s)†A(s)] as a collection of Dirac delta functions and arguing that the integral in Eq. (24) vanishes; this distributional argument is only sketched and does not state precise conditions under which the identity holds. For the diagonal piecewise-linear schedule the identity holds a.e. because A′_ii≠0 only when A_ii∈(0,1), so the reported experiments are not endangered, but the claimed general family of PSD schedules satisfying Assumption 4.1 is not established. Please either give a rigorous proof under explicit assumptions or restrict the theoretical claim to schedules for which the identity can be verified.
- [Appendix E.1, Algorithm 1] Algorithm 1 defines the vector field f element-wise only for i<n and i=n; it does not specify the update rule for masked positions i>n, even though the initial condition contains their latent values and the ODE is solved over the full sequence. Please specify f_i=0 (or an equivalent rule) for masked indices so that the evaluation procedure is fully reproducible.
minor comments (5)
- [Appendix C and §6] Appendix C says 'As the first paper to use diffusion models for TPPs' about Add and Thin, while §6 correctly calls it 'one of the first papers' and Event Flow is also a diffusion-based TPP; please make the wording consistent and accurate.
- [Abstract] The abstract states that the implementation is available at a Github repository, but no URL is provided anywhere in the manuscript; please include the repository link.
- [Figure 4] The y-axis of the long-horizon OTD plots is scaled to magnify differences, but the caption does not state that the axis is truncated; please add a note so the visual gaps are not interpreted as absolute differences.
- [Throughout] There are several typos: 'satisfiyng' in Assumption 4.1, 'trivally' in Appendix G.2, 'e,g.' in Section 2.2, and 'proceeding events' in Section 3.4 should be 'preceding events'; a careful proofreading pass is needed.
- [Remark 4.4] Remark 4.4 states that Euler or RK4 with known x0 and ε restores x0 with zero numerical error; note that this statement does not apply to the conditional forecasting ODE in Eq. (10), where the future x0 is unknown, so the remark should be scoped more carefully.
Circularity Check
No significant circularity: the asynchronous flow-matching objective is a direct extension of standard CFM, the schedule is fixed a priori, and the forecasting ODE conditions on observed latents rather than importing the target results.
full rationale
I walked the derivation chain and found no step in which a claimed prediction or first-principles result reduces, by the paper's own equations, to its inputs. The matrix-valued interpolation in Eq. 5 and the conditional flow matching objective in Eq. 16 are a direct extension of the scalar CFM framework of Lipman et al. (2023), with A(s) fixed a priori as a piecewise-linear diagonal schedule rather than fitted to the evaluation metrics. Eq. 10 is an explicit forecasting ODE that pins observed-event latents to their encoded values y(i) and uses the learned vector field only for the prediction window; this is conditional generation, not a fit renamed as prediction. Proposition A.4 is an argument about equivalence of two vector-field formulations; even if its weak-derivative treatment of the non-invertible schedule is sketchy, that is a correctness risk rather than circularity, and for the actual diagonal schedule the equivalence holds almost everywhere. The only self-citation I found is the related-work mention of Chen et al. (2024b) in the introduction, which is not load-bearing and does not justify any central premise. No uniqueness theorem from the authors' prior work is invoked, no ansatz is smuggled in via citation, and no known empirical pattern is merely renamed. The empirical claims are benchmarked against external baselines on held-out test data. Accordingly, the paper is self-contained with respect to the circularity concerns enumerated in the review instructions, and the appropriate score is 0.
Assumptions & free parameters
free parameters (4)
- Latent dimension d_latent =
32
- VAE KL weight beta_max =
0.01 (with beta_min=1e-5)
- Asynchronous schedule breakpoints s_start(i), s_end(i) =
(N-i)/(2N-1), (2N-i)/(2N-1)
- Maximum sequence length N =
dataset-specific hyperparameter
assumptions (4)
- standard math Flow matching assumptions from Lipman et al. (2023) and Esser et al. (2024) hold for the matrix-valued interpolation: continuity equation and marginalization over conditional paths.
- ad hoc to paper Proposition A.4: A'(s)A(s)^dagger A(s) = A'(s) for non-invertible monotone PSD A(s), with A^dagger the Moore-Penrose inverse.
- domain assumption The beta-VAE latent space is a faithful continuous representation of event times and types, so diffusion in latent space correctly models the joint event distribution.
- domain assumption Causal masking combined with the asynchronous schedule provides correct conditioning for prediction windows.
Cite this review
Pith. "Pith review of ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes." pith.science (2026). https://pith.science/paper/MQ63AZXV
@misc{pith2026250420411,
author = {Pith},
title = {Pith review of: ADiff4TPP: Asynchronous Diffusion Models for Temporal Point Processes},
year = {2026},
howpublished = {\url{https://pith.science/paper/MQ63AZXV}},
note = {Machine review of arXiv:2504.20411}
}
read the original abstract
This work introduces a novel approach to modeling temporal point processes using diffusion models with an asynchronous noise schedule. At each step of the diffusion process, the noise schedule injects noise of varying scales into different parts of the data. With a careful design of the noise schedules, earlier events are generated faster than later ones, thus providing stronger conditioning for forecasting the more distant future. We derive an objective to effectively train these models for a general family of noise schedules based on conditional flow matching. Our method models the joint distribution of the latent representations of events in a sequence and achieves state-of-the-art results in predicting both the next inter-event time and event type on benchmark datasets. Additionally, it flexibly accommodates varying lengths of observation and prediction windows in different forecasting settings by adjusting the starting and ending points of the generation process. Finally, our method shows superior performance in long-horizon prediction tasks, outperforming existing baseline methods.
Figures
Figures from the paper (1 more)
Reference graph
Works this paper leans on
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[1]
The conditional vector field us(xs|ϵ) can be derived in closed form
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[2]
In other words: Eϵ∼N (0,I)[ps(xs|ϵ) ps(xs) us(xs|ϵ)] = us(xs)
The marginal vector fieldus(xs) can be constructed by marginalizing over the conditional vector fieldus(xs|ϵ) that generates the flow. In other words: Eϵ∼N (0,I)[ps(xs|ϵ) ps(xs) us(xs|ϵ)] = us(xs)
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[3]
The training objective for the marginal vector fieldA′(s)vθ(xs,A (s)) can be expressed in terms of the conditional vector fieldus(xs|ϵ). The flowψ(xs|ϵ) in Equation 5 governed by a matrix-valued coefficientA(s)∈ (H 1[0, 1])n×n remains valid as long as the following conditions are met:
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[4]
A(s) is continuous for alls∈ [0, 1]. Proof. We will proceed to show that these conditions are still satisfied. We can expand the conditional vector field as us(xs|ϵ) := A′(s)νs(xs|ϵ) andus(xs) := A′(s)νs(xs). While condition (1) is straightforward, the demonstration of conditions (2) and (3) is remarkably identical to Esser et al. (2024, Appendix B.1)
work page 2024
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[5]
Attentive neural Hawkes process (AttNHP) (Mei et al., 2021)
work page 2021
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[6]
A(s) satisfies the boundary conditions:A(0) = I,A (1) = 0
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[7]
A(s) is positive semi-definite for alls∈ [0, 1]
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[8]
A(s) is monotone non-increasing i.e.∥A(s)x∥≤∥ A(s′)x∥ for all x∈ Rn ifs≥s′
Show all 24 references
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[10]
This condition is trivially satisfied as shown in Proposition A.4
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[11]
The continuity equation provides a sufficient condition to determine ifus(xs) models the evolution of the distribution ps(xs): d dsps(xs) =−∇· [ps(xs)us(xs)] =−∇· [ps(xs)A′(s)νs(xs)]. (25) This equation can be expanded to show that the marginal vector fieldus(xs|ϵ) models the ...
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[12]
To prove this condition, it is first sufficient to show that ⟨A′(s)vθ(xs,A (s)),us(xs)⟩ can be constructed from 13 Asynchronous Diffusion Models for Temporal Point Processes ⟨A′(s)vθ(xs,A (s)),us(xs|ϵ)⟩. Es,ps(xs|ϵ),p(ϵ)⟨A′(s)vθ(xs,A (s)),A′(s)νs(xs|ϵ)⟩ = ZZ ⟨A′(s)vθ(xs,A (s))...
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[13]
Aσmin (s) satisfies the boundary conditions:Aσmin (0) = I,Aσmin (1) = σminI
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[14]
Aσmin (s) is positive definite for alls∈ [0, 1]
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[15]
We define monotone non-increasing in matrices as satisfiyng∥Aσmin (s)x∥≤ ∥Aσmin (s′)x∥ for all x∈ Rn ifs≥s′
Aσmin (s) is monotone non-increasing. We define monotone non-increasing in matrices as satisfiyng∥Aσmin (s)x∥≤ ∥Aσmin (s′)x∥ for all x∈ Rn ifs≥s′
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[16]
Without loss of generality, we can letAσmin (s) be continuous with respect toσmin∈ [0, 1] in the (H 1[0, 1])n×n norm i.e
Aσmin (s) is continuous for alls∈ [0, 1]. Without loss of generality, we can letAσmin (s) be continuous with respect toσmin∈ [0, 1] in the (H 1[0, 1])n×n norm i.e. for allϵ> 0, there exists aδ >0 such that |σmin−σ′ min|<δ =⇒∥Aσmin (s)−Aσmin (s)∥(H 1[0,1])n×n =∥Aσmin (s)−Aσmin ...
2024
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[17]
Recurrent marked temporal point process (RMTPP) (Du et al., 2016)
2016
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[18]
Neural Hawkes Process (NHP) (Mei & Eisner, 2017)
2017
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[19]
Self-attentive Hawkes process (SAHP) (Zhang et al., 2020)
2020
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[20]
Transformer Hawkes process (THP) (Zuo et al., 2020)
2020
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[22]
Intensity-free TPP (IFTPP) (Shchur et al., 2020) Another baseline method we include is Decomposable Transformer Point Processes (DTPP) (Panos, 2024). To ensure fairness in our comparisons, we modify its implementation by training the model to predict the inter-event time direc...
2020
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[23]
This is identical to autoregressive modeling of event sequences
A disjoint noise schedule, where one event is diffused at a time. This is identical to autoregressive modeling of event sequences. The noise schedule is given as: [A(s)disjoint]ii = clip s(i,disjoint) end −s s(i,disjoint) end −s(i,disjoint) start , min = 0, max = 1 ! , where s...
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[24]
This is identical to rectified flow
A synchronous noise schedule, where all events are diffused at the same time. This is identical to rectified flow. The noise schedule is given as: A(s)sync = (1−s)I. 0.0 0.2 0.4 0.6 0.8 1.0 s 0.0 0.2 0.4 0.6 0.8 1.0A(s) Disjoint Matrix A(s)[1,1] A(s)[2,2] A(s)[3,3] A(s)[4,4] A...
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[2020]
cc/paper_files/paper/2020/file/ 4c5bcfec8584af0d967f1ab10179ca4b-Paper
URL https://proceedings.neurips. cc/paper_files/paper/2020/file/ 4c5bcfec8584af0d967f1ab10179ca4b-Paper. pdf. Ho, J., Chan, W., Saharia, C., Whang, J., Gao, R., Gritsenko, A., Kingma, D. P., Poole, B., Norouzi, M., Fleet, D. J., et al. Imagen video: High definition video gener...
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[2021]
Xue, S., Shi, X., Zhang, J., and Mei, H
URL https://openreview.net/forum? id=PxTIG12RRHS. Xue, S., Shi, X., Zhang, J., and Mei, H. Hypro: A hybridly normalized probabilistic model for long-horizon predic- tion of event sequences. Advances in Neural Information Processing Systems, 35:34641–34650, 2022. Xue, S., Shi, ...
2022
Reviewed August 16, 2026 · model on record in the stance chip above.
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