{"id":"70f744b1-f329-4623-89b1-ddbabf45008d","arxiv_id":"2504.20411","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A latent flow-matching model with asynchronous, per-event noise schedules jointly generates inter-event times and event types, improving RMSE and long-horizon optimal-transport distance on five TPP benchmarks.","lead":"ADiff4TPP trains a diffusion model for event sequences where each event is denoised at a different speed, so earlier events are generated first and guide forecasts of later ones. It reports lower errors on next-event and long-horizon benchmarks, but it omits the closest competing baseline and overstates its event-type results.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. 10's forecasting ODE is never shown to sample p(future | observed); the CFM objective only justifies the marginal joint flow, so the empirical claims rest on an unproven inference step.","rationale":"I read the paper's central contribution as the asynchronous matrix-valued flow-matching objective together with the claim that it yields state-of-the-art forecasts. The reader's weakest assumption was Proposition A.4, but for the diagonal piecewise-linear schedule actually used in experiments the identity A'A†A = A' holds almost everywhere, so that proof sketch is not the main threat to the central claim. The more significant gap is the inference-time conditional generation step. The training objective justifies a marginal joint flow for full sequences; it does not, by itself, justify the forecasting ODE in Eq. 10, where observed events are pinned to a single noisy trajectory and the future is generated by an unconditionally trained vector field. The paper provides no theorem or argument showing that this ODE is the probability-flow ODE of the conditional distribution p(future | observed). Since all reported forecasting results are produced by this procedure, the empirical claims are not protected by the theoretical derivation. The reader's other concerns—the abstract's overclaim on event-type SOTA (Table 1 shows worse type error than IFTTPP on Amazon and StackOverflow), the missing Event Flow baseline, and the unavailable code—also support a CONDITIONAL verdict, but the conditional-generation gap is the sharpest technical point to test first.","tokens_in":25180,"tokens_out":26876,"duration_ms":314362,"concrete_test":"Use a low-dimensional Gaussian (or a synthetic TPP with known conditional law). Train a model with the Section 3.2/3.3 objective on joint samples. Verify the unconditional ODE recovers p(x0) as a sanity check. Then fix several test-set y_O, sample many ε, generate futures with Eq. 10, and compare the resulting empirical distribution to the exact p(x_F | y_O) via a two-sample test (e.g., MMD or KS). If the conditional samples deviate while the unconditional marginal matches, Eq. 10 is not the conditional probability-flow ODE and the forecasting pipeline needs an explicit conditioning mechanism.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The CFM objective in Eq. 16 trains vθ to approximate the marginal conditional expectation E[x0−ε | X_s=x_s] of the joint sequence distribution. Forecasting, however, uses the Section 3.4 ODE (Eq. 10), in which observed coordinates are pinned to one forward trajectory x_s^O = A_O(s)y_O + (I−A_O(s))ε_O while future coordinates are driven by vθ. For A_O(s) < I, vθ sees only a noisy observation of y_O; its Bayes-optimal output is an average over the posterior p(y_O | x_s^O), not the conditional mean given the fixed y_O. Nothing in Sections 3–4 proves that solving Eq. 10 yields samples from p(x_F | x0^O = y_O). The paper calls this step \"simple and intuitive,\" and all next-event and long-horizon numbers depend on it. If Eq. 10 is only an inpainting heuristic, the SOTA claim is not backed by the flow-matching derivation. This is more load-bearing than Proposition A.4: for the actual diagonal schedule, A'(s)A(s)†A(s) = A'(s) a.e. because A'_ii ≠ 0 only when A_ii ∈ (0,1), so that equivalence is not the fragile step.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":25447,"tokens_out":9937,"duration_ms":100277,"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":[{"comment":"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.","section":"Abstract and §5.1, Table 1"},{"comment":"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.","section":"§5, Experiments"},{"comment":"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.","section":"§3.4, Eq. (10)"},{"comment":"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.","section":"Appendix A.3, Proposition A.4"},{"comment":"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.","section":"Appendix E.1, Algorithm 1"}],"minor_comments":[{"comment":"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.","section":"Appendix C and §6"},{"comment":"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.","section":"Abstract"},{"comment":"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.","section":"Figure 4"},{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Remark 4.4"}],"recommendation":"major_revision","confidential_remarks":"The asynchronous diffusion idea is potentially interesting and the RMSE/long-horizon results over the included baselines are consistent, but the paper currently overclaims event-type SOTA, omits the closest baseline (Event Flow), and leaves the conditional forecasting step unjustified. These are fixable with additional experiments and either a proof or a more modest claim for Eq. (10). I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: ADiff4TPP is a real method contribution and its long-horizon numbers are consistently good, but the abstract oversells event-type results, Event Flow is absent from the comparison, and Eq. 10's conditional generation has no derivation behind it. I would send it out, but I would expect a heavy revision.\n\nWhat is new: extending flow matching to a diagonal matrix-valued noise schedule for TPPs in latent space. The piecewise-linear per-event schedule means early events are denoised first, and the same model covers next-event and long-horizon windows by choosing start/end times. The CFM objective is standard once you accept A'(s) A(s)^† A(s) = A'(s); for the actual diagonal schedule this identity holds a.e. because A'_ii is nonzero only where A_ii is invertible. Proposition A.4 is sketched in terms of Dirac deltas, which is not rigorous for general PSD schedules, but it is not the fragile part here.\n\nWhere it lands: Table 1 shows strong next-event time results (RMSE) across all five datasets, though event-type error rates are worse than THP on Amazon and IFTPP on StackOverflow. Long-horizon OTD improvements over the included baselines are consistent and get larger with horizon. That is the paper's real punch.\n\nSoft spots:\n- Missing Event Flow. It is cited in related work, it is the same technical family (flow matching for TPPs, one denoising pass for the horizon), and it is not in any table. SOTA claims are unearned without it.\n- Abstract overclaims: 'state-of-the-art ... event type' is false on two of five datasets.\n- The load-bearing gap is Eq 10. vθ is trained to approximate E[x0 - ε | x_s] for the marginal joint flow. At inference observed coordinates are pinned with the true y, but vθ only sees noisy x_s^O and cannot separate y from ε; its output for future coordinates averages over possible observed y. Solving Eq. 10 produces an inpainting heuristic, not a proven sample from p(future | observed). This may be fine empirically, but the paper presents it as derived ('simple and intuitive'). Either prove it for diagonal schedules or reframe and ablate against conditional training / classifier-free guidance.\n- Minor: no working code link despite the abstract saying so; DiT training hyperparameters not given; Algorithm 2 starts at x1=ε while Section 3.4 starts at s_end = max s_end(i), a small inconsistency.\n\nSerious thinker: yes. The experiments look honestly run (five seeds, standard deviations, ablations for VAE dim and schedules). Citation pattern is fine; self-cites are mostly prior asynchronous diffusion methods.\n\nWho benefits: anyone working on diffusion/flow models for event sequences or long-horizon TPP forecasting. For peer review: accept conditional, not desk reject. Referees should push for Event Flow, corrected claims, and either a proof or a candid heuristic framing of Eq 10.","headline":"A useful asynchronous flow-matching recipe for TPP long-horizon forecasting, held back by an unproven conditioning step and a missing key baseline.","tokens_in":25997,"tokens_out":6392,"would_cite":true,"duration_ms":71439,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["asynchronous diffusion","temporal point processes","conditional flow matching","matrix-valued noise schedules","event sequence forecasting","long-horizon prediction","latent diffusion","diffusion transformer"],"falsifier":"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 $\\sigma_{\\min} \\to 0$.","tokens_in":24944,"feed_emoji":"🕒","tokens_out":15841,"duration_ms":131252,"temperature":0.7,"pith_summary":"This paper claims that temporal point processes — event streams like purchases, retweets, taxi pickups, or medical observations — are better modeled by a diffusion process that corrupts and restores events at different speeds than by one that treats all events alike. The specific mechanism is to denoise earlier events first, so that by the time the model generates a later event, it is conditioning on a clean, already-generated past instead of on noise. The authors derive a training objective for this asynchronous setup by extending conditional flow matching to matrix-valued noise schedules, and combine it with a variational autoencoder that turns each event's mixed continuous-and-categorical content into a continuous vector. On five benchmark datasets they report lower inter-event-time error than all baselines (for Retweet, 17.88 versus 21.71), better or competitive event-type accuracy, and long-horizon forecast distances that improve by an average of 24.5% over prior methods, with the gap growing as the horizon lengthens.","feed_headline":"24.5% better long-horizon forecasts with staggered diffusion","feed_subtitle":"Diffusing later events into noise first lets one model predict the next event and the next thirty in a single pass.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the conditional flow matching framework and the conditional probability path formula (their Eq. 13) that the paper extends to matrix-valued schedules.","marker":"Lipman et al., 2023"},{"why":"The prior asynchronous diffusion approach (groupwise diffusion) that the paper explicitly extends to a more flexible, customizable family of noise schedules.","marker":"Lee et al., 2023"},{"why":"Provides the flow-conditioned-on-noise notation used throughout, and the argument in their Appendix B.1 that the marginal vector field proof of Lemma 4.2 is modeled on.","marker":"Esser et al., 2024"},{"why":"The diffusion transformer architecture that $v_\\theta$ is built from, with the schedule matrix replacing the timestep embedding.","marker":"Peebles & Xie, 2023"},{"why":"The latent diffusion paradigm the paper follows to handle mixed continuous and discrete event data.","marker":"Rombach et al., 2022"},{"why":"The $\\beta$-VAE latent encoding scheme with cyclic $\\beta$ regularization that the paper adapts to map event attributes into continuous latents.","marker":"Zhang et al., 2024"},{"why":"Supplies the five benchmark datasets, the baseline implementations, and the RMSE/error-rate evaluation that the paper's state-of-the-art claims are measured against.","marker":"Xue et al., 2024"},{"why":"Defines rectified flow, which the paper's synchronous schedule is identical to, making it the key ablation baseline.","marker":"Liu et al., 2023"},{"why":"The closest prior flow-matching treatment of TPP forecasting with a single denoising pass, positioning the paper's contribution.","marker":"Kerrigan et al., 2024"},{"why":"The first diffusion-based TPP baseline the paper must beat on both next-event and long-horizon tasks.","marker":"Lüdke et al., 2023"}],"fun_headline_variants":["Asynchronous diffusion model forecasts 30 events ahead in one pass","Staggered noise schedule beats baselines on long-horizon event prediction","One diffusion model handles next event and 30-step forecasting","Asynchronous noise ordering improves temporal point process forecasts","Diffusion with staggered noise predicts event sequences further ahead"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Asynchronous diffusion model forecasts 30 events ahead in one pass","Staggered noise schedule beats baselines on long-horizon event prediction","One diffusion model handles next event and 30-step forecasting","Asynchronous noise ordering improves temporal point process forecasts","Diffusion with staggered noise predicts event sequences further ahead"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000357,"raw_usage":{"total_tokens":2030,"prompt_tokens":1137,"completion_tokens":893,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":753,"completion_tokens_details":{"reasoning_tokens":810}},"tokens_in":753,"tokens_out":893,"duration_ms":7629,"temperature":1.0,"reasoning_tokens":810,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:30:14.874938+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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 $\\sigma_{\\min} \\to 0$.","supporting_citations":[],"review_version":1}