Edit-Based Flow Matching for Temporal Point Processes
Authors: David Lüdke
Marten Lienen
Marcel Kollovieh
Stephan Günnemann
Venue: ICLR 2026 Poster (2026)
Keywords: Generative Modelling
Forecasting
Events
Sequences
Sets
Continuous Time
CTMC
Primary area: generative models

Abstract: Temporal point processes (TPPs) are a fundamental tool for modeling event sequences in continuous time, but most existing approaches rely on autoregressive parameterizations that are limited by their sequential sampling. Recent non-autoregressive, diffusion-style models mitigate these issues by jointly interpolating between noise and data through event insertions and deletions in a discrete Markov chain. In this work, we generalize this perspective and introduce an Edit Flow process for TPPs that transports noise to data via insert, delete, and substitute edit operations. By learning the instantaneous edit rates within a continuous-time Markov chain framework, we attain a flexible and efficient model that effectively reduces the total number of necessary edit operations during generation. Empirical results demonstrate the generative flexibility of our unconditionally trained model in a wide range of unconditional and conditional generation tasks on benchmark TPPs.

Published as a conference paper at ICLR 2026
EDIT-BASED FLOW MATCHING FOR TEMPORAL POINT PROCESSES
David Lüdke", Marten Lienen', Marcel Kollovich, Stephan Günnemann fd. [u.kue m. wienen, m. wolkkollliiet s guennemann um. de School of Computation, Information and Technology & Munich Data Science Institute Technical University of Munich
ABSTRACT
Temporal point processes (TPPs) are fundamental tool for modeling event quences in continuous time, but most existing approaches rely on autoregres- sive parameterizations that are limited by their sequential sampling. Recent non- autoregressive, diffusion-style models mitigate these issues by jointly interpolating between noise and data through event insertions and deletions in a discrete Markov chain. In this work, we generalize this perspective and introduce an Edit Flow process for TPPs that transports noise to data via insert, delete, and substitute edit operations. By learning the instantaneous edit rates within a continuous-time Markov chain framework, we attain a flexible and efficient model that effectively reduces the total number of necessary edit operations during generation. Empirical results demonstrate the generative flexibility of our unconditionally trained model in wide range of unconditional and conditional generation tasks on benchmark TPPs.
INTRODUCTION
Temporal point processes (TPPs) capture the distri- bution over sequences of events in time, where both the continuous arrival-times and number of events random. They are widely used in domains such as finance, healthcare, social networks, and trans- portation, where understanding and forecasting event dynamics and their complex interactions is crucial. Most (neural) TPPs capture the complex interactions between events autoregressivelly parameterizing a conditional intensity/denssty of each event given its history (Daley & Vere-Jones, 2006; Shchur et al., 2021). While natural and flexible, this factorization comes with inherent limitations: sampling scales lin- early with sequence length, errors can compound in multi-step generation, and conditional generation is restricted to forecasting tasks.
to
0.11
0.95
to.0
0.11
0.50
0.95
ins
del
t0.19
0.11
0.21
0.50
]
t.55
0.11
0.21
0.51
sub
0.73
0.11
0.21
0.51
del
0.21
0.51
Figure 1: Edit process transporting to ~
Proise (t) to i, ~ Quaget (t) by inserting, delet- ing and substituting events.
Beyond autoregression. Recent advances demon- strate that modeling event sequences jointly proposes sound alternative overcome these limitations. Inspired by diffusion, ADDTHINN (Lüdke et al., 2023) and PSDIFF (Lüdke et al., 2025) leverage the thinning and superposition properties of TPPs to construct discrete Markov chain that learns to transform noise sequences to Pnoise (t) into data sequences i ~ Uurgee (t) through insertions and deletions of events. These methods highlight the promise of joint sequence modeling for TPPs by learning stochastic set interpolations and have shown state-of-the- art results, especially in forecasting.
In parallel, Havasi et al. (2025) introduced Edit Flow, a discrete flow-matching framework (Gat et al., 2024; Campbell et al., 2024; Shi et al., 2025) for variable-length sequences of tokens (e.g..
"Equal contribution
Find the code w...cittum.de//dml/eeiii

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Published as a conference paper at ICLR 2026
language). Their approach models discrete flows in sequence space through insertions, deletions, and substitutions, formalized as a continuous-ting Markov Chain (CTMC). To make the learning process tractable, they introduce expanded auxilliary state space that aligns sequences, simultancously reducing the complexity of marginalizing over possible transitions and enabling efficient element-wise parameterization in sequence space.
In this paper, we unify these perspectives and propose EDITPP, an Edit Flow for TPPs that learns to transport noise sequences to Phoise (t) to data sequences 1 (harge(() via atomic edit operations insertions, deletions, and substitutions (see figure 1). We define these operations specifically for TPPs, efficiently parameterize their instantaneous rates within a CTMC, propose an auxiliary alignment space for TPPs. and show that our unconditionally trained model can be flexibly applied to both unconditional and conditional tasks with adaptive complexity. Our main contributions are:
We introduce EDITPP, the first generative framework that models TPPs via continuous- time edit operations, unifying stochastic set interpolation methods for TPPs with Edit Flows for discrete sequences.
We propose tractable parameterization of insertion, deletion, and substitution rates for TPPs within the CTMC framework, effectively reducing the number of edit operations for generation.
We demonstrate empirically that EDITPP achieves state-of-the-ard results in both unconditional and conditional tasks across diverse real-world and synthetic datasets.
BACKGROUND
2.1
TEMPORAL POINT PROCESSES
TPPs (Daley Vere-Jones, 2006; 2007) are stochastic processes whose realizations are almost surely finite, ordered sets of random events in time. Let t [t with t(9) [0, denote realization of n events on bounded time interval, which can equivalently be represented by the counting process (t) Σ
i=1 1(t(0) < f} counting the number of events up to time t. A TPP is
uniquely characterized by its conditional intensity function (Rasmussen, 2018):
E[[N(L At) N(L) H,]
(²)1)= lim A410
(1)
At
where H. -(66)
(() < t} denotes the history up time t. Intuitively, (t) represents the instantaneous rate of events given the past. Two important properties of TPPs are superposition and thinning. Superposition, i.e., inserting realizations from TPPs with intensities x1 and X2, results in a sample from a TPP with intensity = A A2 Independent thinning, i.e., randomly deleting any event of sequence from a TPP with intensity X with probability p. results in an event sequence from a TPP with intensity (1 p)
sequence into another, t = t1 U 12, where t and to
The likelihood of observing
sequence given the conditional intensity/density is:
n II p((0)) Hacs) (1 F(T Hoo))
n (I()) exp (-f" T (x(ssss) (2)
p(t)
where F(T He) is the CDF of the conditional event density p(t H₂). While this autoregressive formulation of TPPs provides a natural framework for modeling event dependencies, it also poses challenges. Parameterizing the conditional intensity or density is generally nontrivial, and the inherently sequential factorization can lead to inefficient sampling, error accumulation, and limits conditional tasks to forecasting (Lüdke et al., 2023; 2025).
2.2 MODELING TPPs BY SET INTERPOLATION
Instead of explicitly modeling the intensity function, Lüdke al. (2023; 2025) leverage the thinning and superposition properties of TPPs to derive diffusion- generative models that interpolate between data event sequences t Qurren (t) and noise to Pnoise (t) by inserting and deleting
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elements. ADDTHIN (Lüdke al., 2023) defines the noising Markov chain recursively over fixed number steps with size indexed by E [0, as follows:
(t agAs- att)
a.) (o))
( Thin
(ii) Add
where A1 (4) is the unknown target intensity of the TPP and ar, E (0,1). Intuitively, this noising process increasingly deletes events from the data sequence, while inserting events from a noise TPP (t). PSDIFF (Lüdke et al., 2025) further separates the adding and thinning yield Markov chain for the forward process, that stochastically interpolates between to and t as follows:
Pt 1 to)
[I
II LEE
a iftet a. if to
(4)
or equivalently (t) (a)1 + ao) with â, being the product of ag's 's. Eq. (4) defines an element-wise conditional path by independent insert and delete operations on TPPs, assuming to nut 11 = 0.
2.3 FLOW MATCHING WITH EDIT OPERATIONS
Havasi et al. (2025) introduce Edit Flows, non-autoreerressive generative framework for variable- length token sequences with a fixed, discrete vocabulary (e.g., language). They propose discrete flow that transports a noisy sequence Ep Pnoise (x) to data sequence æ1 ~ Adata (x) via elementary edit operations: insertions, deletions, and substitutions. This is formalized via the discrete flow matching framework (Gat et al., 2024; Campbell et al., 2024; Shi et al., 2025) in an augmented space, yielding a CTMC Pr(X,+* = x Xg = xx) = 8z, (x) + hu (a x.) + (h) with transition rates u governed by the edit operations.
Directly defining a conditional rate u, (z [z) x.)) to match u to, as in discrete flow matching, is very hard or even intractable, since all possible edits producing must be considered. Thus, to train this CTMC, they rely on two major insights. First, a CTMC in a data space X' can be learned by introducing
augmented space X' Z where the true dynamies
known. Second,
designing the auxiliary space 2 to follow the element wise mixture probability path p=(z 20, 21
II. [[1 K. )5 so (2()) + kgō (e) [=() with kappa schedule K2 E [0, 1] (Gat et al., 2024) enables training the CTMC directly in the data space X' of variable-length sequences.
Edit operations are encoded by introducing, a blank token c and mapping (æg, 21) into aligned sequences (zp, 21 in Z, where pairs (=)") 21 ) correspond to insertions 2), deletions (x,c), c). or substitutions (x, y). Crucially, since the discrete flow matching dynamics in Z are known, they can be
transferred back to X' via p. (xx, z zo, 21 P=(= 20, 21 (1) (x) by removing e's with
flm-blanks- Then, the marginal rates a are learned X' by marginalizing over with the Bregman divergence
L where 0(2,, i, 2 ((0) www.hlankss ((21 3.
E (20,21))T(20,2))) 0t,
Σ ug (x xT.))
Σ
h
log ug (æ(2z,, 21) mm)))
(5)
1 Kis
(4) #2
(i-1) (1)
(i+1)
2...,22 (n))):
3 METHOD
We introduce EDITPP, an Edit Flow process for TPPs that directly learns the joint distribution of event times. Our process leverages the three elementary edit operations insert, substitute, and delete to define a CTMC that continuously interpolates between two event sequences to ~ Pnoise (t) and Vdaal(t).
Let T =
0.. T denote the support of the TPP. We define the state space as X7 = U
))...., {(,) T) E T" < {()) <... < f(t) < T), denoting the set of all pos- ...., sible padded TPP sequences with finitely many events. Note that the padding values are introduced for notational simplicity when defining the edit operations on T.
(0, +() f
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sub 3.1)
ss
Ls
(1)
Ls
(2)
ins(ts, f)
del(ts. 4)
28
Figure 2: Our discrete edit operations transform continuous event sequences through insertions, substitutions and deletion.
3.1 EDIT OPERATIONS
Our model navigates the state space XT through set of atomic edit operations. While Edit Flow was originally defined for discrete state spaces, we can generalize the method to continuous state spaces provided that the set of edit operations remains discrete. We achieve this by defining finite set of edit operations on our continuous state space Xy that nonetheless allow us to transition from any sequence t to any other t' through repeated application.
Similar to Havasi et al. (2025), we design our operations to be mutually exclusive: if two sequences differ by exactly one edit, the responsible operation is uniquely determined. This simplifies the parameterization of the model and computation of the Bregman divergence in Eq. (5).
Insertion: To discretize the event insertion, quantize the space between any adjacent events (() and ((+1) into bins evenly-spaced bins. Then, we define the insertion operation relative to the ith event as
(ns(t,i,j) (100 (10) (0)) J j-1+a (1(++1) (10), ((441)
((++1)
(6)
bins
for i E dequantization in likelihood-basse generative models (Theis al., 2016). The boundary elements (()) and g(n++) T ensure that insertions possible across the entire support T. Since the bins between different are non-overlapping, insertions are mutually exclusive.
E [bins] where a (4(0, 1) is a dequantization factor inspired by uniform
Substitution:
We implement event substitutions by discretizing the continuous space around each event into bub bins. In this case, the bins are free to overlap, since a substitution always uniquely determined by the substituted event. We choose maximum movement distance d and define
sub(t, i, sort (1E ((-1) ((+1)
(n+1)) (00) (0))
for E (I....,.), E [bann), where 710) = [1(() 8 1-1+228 is the updated event restricted to the support T and, again, ~ L((0 1) is uniform dequantization factor within the j-th bin.
Deletion: Finally, we define removing event i [1.....n] straightforwardly as
del(t, = (E ()-1)) ((+1) ((+t),..., (1+1)).
(8)
In combination. these operations facilitate any possible edit of event sequence through insertions and deletions with substitutions as a shorteut for local delete-insert pairs. Note that we neither allow inserting after the last boundary event nor substituting or deleting the first or last boundary events, thus guaranteeing operations to stay in the state space XT. We illustrate the edit operations in Fig. 2.
Our choice of ins, sub and del ensures three key properties: (i) the resulting event sequences remain valid TPPs, (ii) the number of valid operations, e.g. ins(t, . is independent of the position i, which is necessary for efficient parameterization, and (iii) at most one unique operation can transition between any states, which significantly reduces the complexity of the training loss in Section 3.3. While these properties are comparably simple to achieve for token sequences in language modeling (Havasi et al., 2025), where any token replace any other, they require special care in the case of
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TPPs. del and sub are defined to ensure that the resulting event sequence remains in increasing order and that the padding events ((0) and g(++1) remain in place. del transitions are unique because the removed event determines exactly which deletion occurred. Similarly, sub transitions are unique because the original position of the substituted event disambiguates the operation, even though two distinct sub operations may yield the same substituted event value. To achieve uniqueness for ins, the insertion bins corresponding to its(t, have to be mutually disjoint for any i. since insertions lack a removed event to disambiguate them. We achieve this by sizing the bins relative to the distance between (6) and ((++1)
Generating new event sequence in the Edit Flow framework then means to emit a continuous stream of edit operations by integrating a rate model u (- t) from 8 = 0 to 1. The emitted operations transform noise sequence to into data sample i by transitioning through a series of intermediate states t. Given a current state ta we parameterize the transition rates as
Parameterization
u (ins(ts; (. t,) (t. (t.) Q.A(( tt).
u (sub(t,, (, { t.) = (t,) Q (j tt),
(10)
" (del(t,))) i) t.) (t.))
(11)
8,17 where Adel Xins Aghh denote the total rate of each of the three basic operations at each event ((0 The
distributions Q and Q are categorical distributions over the discretization bins j E [Mmms] and
j E [bsub], respectively. They distribute the total insertion and substitution rates between the specific options.
3.2 AUXILIARY ALIGNMENT SPACE
Training our rate model ug by directly matching marginalized conditional rate u, &1 to) generating (t(t &1, to), as common in discrete flow matching (Campbell et al., 2024; Gat et al., 2024), is challenging
even intractable for Edit Flows, since it would require accounting for all possible edits that could produce t (Havasi et al., 2025).
To address this, following Havasi et al. (2025), we introduce auxiliary alignment space for TPPs, where every possible edit operation is uniquely defined in the element wise mixture path 2, (2. 20, 21), making the learning problem tractable.
tp
0.0
0.11
0.50
0.95
Zo
0.50
del
sub
del
In language modeling, any token appear in any position, Havasi et al. (2025) achieve strong results even when training with simple alignment that juxtaposes two sequences after shifting one of them by constant number of places. In our case, for the alignments correspond possible edit operations, two events can only be matched, i.e., (t) * and 21" * E, if (9) 2("| < 5 since 20 otherwise the resulting sub operation would be invalid. Furthermore,
0.0
0.21
0.55
f
n.0
n.21
0.55
Figure 3: Illustration of the alignment space for to and t,-
zs have to correspond to sequences in Xr, so frm-blanks (z) has to be increasing, and in particular any mixing 2g between 2g and y needs to be valid, i.c., 2, ~ (z. zo, 21) + frm-blanks(Zz) E Xy.
We find the minimum-cost alignment between the non-boundary events of to and ti with the Boadleman-Wunsel algorithm (Needleman Wunsch, 1970), i.e..
align(to, t wrap boundaiiss Needleman- (g (Im) ((lm)) Cass Csub; cas) ,
(12)
and the cost functions
1160 - 11)
if 1 1191 < and 1/ (i-1) < <(10) (1) < 2 (1+1)
Csub (t, =
00
otherwise
(13)
if R
if 10) > 10
Cins (i.
(aali,
2
otherwise
8o
otherwise
where trap-boundaries wraps the sequences with aligned boundary events 0 and T. The algorithm builds up the aligned sequences pair by pair. The operations corresponds to adding different pairs to the end of (zo: 21), i.e., insertion (c, deletion (16") and substitution (16" ((")) (see Fig. 3).
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We carefully craft the cost functions in Eq. (13), to guarantee that the minimum-cose alignment corresponds ins, sub and del operations as we define them in Section 3.1. With the (t - - < condition in Csub, ensure that the aligned sequences will never encode sub operation for two events that are further than apart. The costs for insertions and deletions and the additional con- dition Csub, ensure that the aligned sequences are jointly sorted, ie.. for any < we have max (20 21 < min 1 2²)") where min and max ignore e tokens. This means that any in- terpolated 2, is sorted by construction. The validity of encoded ins and del operations follows immediately.
3.3 TRAINING
We train model (. t.) by optimizing the Bregman divergence in Eq. (5). This amounts to sampling from a coupling π < z1) in the aligned auxiliary space and then matching the ground- truth conditional event rates. Note that the coupling (= 21) is implicitly defined by its sampling procedure: sample to, t ~ x(to. {1) from a coupling of the noise and data distribution, e.g., the independent coupling (too, t1) p(fo) q(t)), and then align the sequences 20. ø1 align(to. t1). For our choice of operations, the divergence is
Σ WE)(L,
(w tx)
E
Es log uggu (2) (t)). (14)
(9)
(30.51))T( F0:1)
1-K,
where (ttt)) is the set of all edit operations applicable to t, and (25
=0(0) is the edit operation encoded in the i-th position of the aligned sequences 2, and ø1. To make it precise, we have
(ins(t,, (, | | {0} U [n].J] E [bms]} {sub(t,, i,j) i [m], E [bmab]] (del(t,, i [n]]]
l(t.) = UU
(15)
and
(',
if 22 = and
2 * E, x (1) 4 E,
w (22!"
sub(ts, v,,'') del(t,, 1')
if 2 (1) and
(16)
if + and 21 c.
is the index such that blank (z+) maps 24 to as with the convention that e is mapped to the same i' as the last element of z, before that not is the index of the insertion substitution bin relative to (x') that 2f falls into.
3.4 SAMPLING
Algorithm 1: Conditional Sampling
Input:
Sampling from model is done by for- ward simulation of the CTMC from noise We fol- low (Havasi et al., 2025; Gat et al., 2024) and leverage their Euler approximation, since exact simulation is intractable. Even though the rates are parameterized per el- ement, sampling multiple edits within a time horizon can be done in parallel. At each step of length h, insertions posi- tion i occur with probability h Aim (t) and deletions or substitutions occur with proba- bility h(ddd (t) + A (t)). Since they are mutually exclusive the probability of sub- stitution vs deletion is Agth (t)/(Aaab + end Return: forecast trajectory C" (²(t,=1)
condition t C(t,), noise to ~ Proise h = 1/ Nsteps (=f. 2f) align(C(ta)) tf)
to Pnoise (t) up to
while 8 < do
Euler update
Sample edits wa ~ h (- te)
tath apply we to t,
Recondition
2c (. 26 2f) 1 +- f-mm-blaukk 8 (
Merge
tr +- ('((tt)) U
s 1
(t). (t)). Lastly, the inserted or substituted events are drawn from the respective dis-
tributions Q to update t,. For short sum-
mary of the unconditional sampling step refer to the Euler update step depicted in algorithm Algo-
rithm

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Published as a conference paper at ICLR 2026
Conditional sampling. We can extend the unconditional model conditional generation given binary mask on time c: 7 + {0, 1) (e.g.. for forecasting, <(t) = t I fhistryy) ). For sequence t, we define the conditioned part Ctt) (t t c(t) 1} and its complement C* (t). Then depicted in algorithm Algorithm 1, for conditional sampling, we can simply enforce the conditional subsequence to follow noisy interpolation between Ej C(to) and ti = C(t)), while the complement evolves freely in the sampling process.
3.5 MODEL ARCHITECTURE
For our rate model (- | 2s), we adapt the Llama architecture, a transformer widely ap- plied for variable-length sequences in language modeling (Touvron al., 2023). We employ FlexAttent in the Llama attention blocks, which supports variable-length sequences na- tively without padding (Dong et al., 2024). As a first step, we convert the scalar event sequence æ, into sequence of token embeddings by applying MI.P(SnEEbbzz' /T)) to each to each event, where ML.P refers to a small multi-layer perceptron (MIP) and Sin is a sinusoidal embedding (Vaswani et al., 2017). We convert and |.a into two additional tokens in equivalent way with separate MLPs and prepend them to the embedding sequence, which we then feed to the Llama. Lastly, we apply one more MLP to map the output embedding h() In particular, we parameterize
of each event to transition rates.
8.1 exp(AM tanh (8) ))
A exp(AM tanh(h
Adel exp(AM tanh(h (1)),
(17)
QUs softmax (1 jins Q.is).
Q softmax(h
(18)
We list the values of all relevant w hyperparameters in Appendix A.
4 EXPERIMENTS
We evaluate our model seven real-world and six synthetic benchmark datasets (Omi et al., 2019; Shchur et al., 2020b; Lüdke et al., 2023; 2025). In our experiments, we compare against IFTPP (Shchur et al., 2020a), autoregressive baseline which consistently shows state-of-the- performance (Bosser & Taieb, 2023; Lüdke et al., 2023; Kerrigan et al., 2025). We further compare to PSDIFF (Lüdke al., 2025) and ADDTHIN (Lüdke al., 2023), given their strong results in both conditional and unconditional settings and their methodological similarity to our approach. All models are trained with five seeds and we select the best checkpoint based on W1-over-dIET against a validation set. EDITPP, ADDTHIN, and PTD are trained unconditionally but can be conditioned inference time.' We list the full results Appendix E.3.
For forecasts, we compare predicted and target sequences by three metrics: dxiso introduced by Xiao al. (2017), the mean relative error (MRE) of the event counts and dIET, which compares inter-event times to quantify the relation between events such as burstiness. In unconditional generation, we compare our generated sequences to the test set terms of maximum mean discrepancy (MMD) (Shchur et al., 2020b) and their Wasserstein-1 distance with respect to their counts (d)) and inter-event times (dIET). See Appendix for details.
4.1 UNCONDITIONAL GENERATION
To evaluate how well samples from each TPP model follow the data distribution, we compute distance metrics between 4000 sampled sequences and hold-out test set. We report the unconditional sampling results in Table 1. EDITPP achieves the best rank in unconditional sampling by strongly matching the test set distribution across all evaluation metrics, outperforming all baselines. The autoregressive baseline IFTPP shows very strong unconditional sampling capability, closely matching and some dataset and metric combination outperforming the other non-autoregressive baselines ADD ADDTHIN and PSDIFF.
'To stay comparable, employ the conditioning algorithm from Lüdke al. (2025) for ADDTHIN.
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Table Unconditional sampling performance. Bold is best, underlined second best. Ranking follows full results in Appendix E.3 and results are grouped if they fall within the std of the best member.
H1
H2
NSP
NSR
SC
SR
PG
R/C
R/P
Tx
Tw
Y/A
Y/M
IFTPP
1.6
1.2
3.2
3.9
6.7
1.2
16.2
7.5
2.0
5.0
2.6
5.8
2.9
ADDTHIN
2.4
1.8
3.5
15.7
24.6
2.5
4.6
63.0
10.2
4.1
4.4
11.8
3.7
MMD
PSDIFF
3.3
1.8
2.0
5.9
19.8
2.4
3.2
6.5
1.0
3.8
3.4
4.1
3,4
EDITPP
1.1
1.2
1.7
3.5
7.7
1.0
1.4
8.2
2.4
3.1
1.3
3.7
4.0
IFTPP
20.5
13.3
11.5
14.1
1.5
23.0
294.6
3.9
3.2
2.9
6.5
3.3
2.5
ADDTHIN
33.3
21.8
12.8
49.0
22.7
41.8
24.5
37.0
33.6
2.3
15.5
6.0
1.6
W1.h
PSDIFF
26.9
29.6
5.5
13.3
10.6
30.3
16.1
1.3
2.5
2.8
6.3
1.5
1.5
EDITPP
7.6
7.0
3.1
1.5
1.3
6.4
6.2
1.9
5.7
2.5
3.4
1.4
1.7
XI0
xte
X10-2
x0002
X30-
X
X
XII
XIP
X
X
X
X30P
IFTPP
6.3
5.8
3.2
2.3
6.5
7.1
30.3
1.8
7.1
17.4
4.9
3.2
2.8
W W.AET
ADDTHIN
6.6
7.0
3.2
3.9
15.1
9.4
8.0
5.3
20.0
8.8
5.5
3.2
2.4
PSDIFF
8.6
9.9
3.0
5.1
32.6
12.8
9.0
1.6
4.3
11.1
6.7
2.4
2.3
EDITPP
5.3
5.5
3.1
2.2
6.4
7.0
7.5
1.4
6.0
11.1
4.6
2.5
2.3
X10
K10
X10
X30
4.2 CONDITIONAL GENERATION (FORECASTING)
Predicting the future given some history window is fundamental TPP task. For each test sequence, we uniformly sample 50 forecasting windows [To. 7), To [AT, AT), with minimal history and forecast time AT. While, this set-up is very similar to the one proposed by Lüdke et al. (2023), there are key differences: we not fix the forecast window and do not enforce a minimal number of forecast history events. In fact, even an empty history encodes the information of not having observed an event and TPP should capture the probability of not observing any event in the future.
We report the forecasting results in Table 2. EDITPP shows very strong forecasting capabilities closely match- ing or surpassing the baselines across most dataset and metric combina- tions. Even though IFTPP is explic- itly trained auto-regressively pre- dict the next event given its history, it shows overall worse forecasting capa- bilities compared to the uncondition- ally trained EDITPP, ADDTHIN and PSDIFF. This again, underlines pre- vious findings (Lüdke et al., 2023), that autoregressive TPPs can suffer from error accumulation in forecast- ing. Similar the unconditional set- ting, PSDIFF (transformer) outper- forms ADDTHIN (convolution with circular padding), which showcases the improved posterior and modeling of long-range interactions.
Forecasting accuracy up to T. Bold is best, un- derlined second best. Ranking follows full results in Ap- pendix E.3 and results are grouped if they fall within the of the best member.
Table 2:
PG
R/C
R/P
Tx
Tw
Y/A
Y/M
IFTPP
6.0
3.9
6.3
4.7
2.6
1.8
3.4
ADDTHIN
2.5
8.8
7.3
4.0
2.8
1.5
2.9
dxiso
PSDIFF
2.4
3.2
4.8
4.4
2.6
1.5
3.0
EDITPP
2.5
3.4
4.9
4.5
2.7
1.5
3.0
X_0
X10
IFTPP
38.9
7.5
3.5
3.2
2.1
3.7
3.9
ADDTHIN
3.7
14.8
4.6
3.0
3.0
3.5
3.7
MRE
PSDIFF
3.4
3.3
3.0
11.4
2.4
3.5
9.2
EDITPP
3.5
3.6
2.8
12.3
2.3
3.5
9.0
X:0-1
X3D04
IFTPP
4.7
6.8
14.7
1.4
2.2
5.9
3.9
ADDTHIN
4.0
6.9
10.3
1.2
1.5
4.9
2.6
dIET
PSDIFF
4.1
6.2
9.5
1.1
1.5
4.9
2.6
EDITPP
4.0
6.8
10.1
1.4
5.0
2.7
4.3 EDIT EFFICIENCY
The sub operation allows our model to modify sequences in more targeted way when compared to PSDIFF or ADDTHIN, which have to rely on just inserts and deletes.
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Rodkit Posts
Reddit Comments
0.4
1.0
dum
MMD
0.3
0.2
0.5
0.0
64
128
256
16
52
125
256
16
64
125
256
Steps
Steps
Steps
K
Figure 4: Changing the number of steps it allows trading off compute and sample quality in terms of di, dIET and MMD at inference time.
Note that one sub operation can replace an insert- delete pair. Table shows this results EDITPP using fewer edit operations than PSDIFF aver- age even if one would count substitutions twice, insert and delete. This is further ampli- fied by the fact, that unlike EDITPP, PSDIFF and ADDTHIN only indirectly parameterizes the tran- sition edit rates by predicting & by insertion and deletion at every sampling step.
Table Average number of edit operations in unconditional sampling across datasets. Full re- sult Table 13.
Ins
Del
Sub
Total
PSDIFF EDITPP
173.48
61.04
0.00
234.52
137.42
33.08
29.16
199.65
In Table 4, we compare their actual sampling run- time for batch size of 1024 on the two dataset with the longest sequences. Our implementation beats the reference implementations of ADDTHIN and PSDIFF by large margin. Note, that for fair comparison, we fixed the number of sam- pling steps to 100 in all previous evaluations. As continuous- time model, EDITPP can further trade off compute against sample quality at inference time without retraining, in contrast discrete-time models like ADDTHIN and PSDIFF. Fig. 4 shows that sample quality improves as we increase the number of sampling steps and therefore reduce the discretization step size of the CTMC dynamics. At the same time, the figure also shows rapidly diminishing quality improvements, highlighting potential for substantial speedups with only minor quality loss.
Table 4: Sample run-time (ms)
H100 GPU.
R/P
R/C
ADDTHIN 18,075.62
17,689.36
PSDIFF 7,776.35
3,913778
EDITPP 4,120.38
1,505.68
5 RELATED WORK
The statistical modeling of TPPs has long history (Daley & Vere-Jones, 2007; Hawkes, 1971). Classical approaches such as the Hawkes process define parametric conditional intensities, but their limited flexibility has motivated the development of neurally parameterized TPPs:
Autoregressive Neural TPP: Most neural TPPs adopt an autoregressive formulation, modeling the distribution of each event conditional on its history. These models consist of components: history encoder and an event decoder. Encoders are typically implemented using recurrent neural networks (Du et al., 2016; Shchur al., 2020a) or attention mechanisms (Zhang et al., 2020a; Zuo et al., 2020; Mei et al., 2022), with attention-based models providing longer-range context at the cost of higher complexity (Shchur et al., 2021). Further, some propose to encode the history of TPP in continuous latent stochastic processes (Chen et al., 2020; Enguchard et al., 2020; Jia & Benson, 2019; Hasan et al., 2023). For the decoder, a wide variety of parametrizations have been explored. Conditional intensities related measures (c.g.. hazard function or conditional density), can be modeled, parametrically (Mei & Eisner, 2017; Zuo et al., 2020; Zhang et al., 2020a), via neural networks (Omi et al., 2019), mixtures of kernels (Okawa et al., 2019; Soen et al., 2021: Zhang et al., 2020b) and mixture distributions (Shchur et al., 2020a). Generative approaches further enhance flexibility: normalizing flow-based (Shchur et al., 2020b), GAN-based (Xiao al., 2017). VAE-based (Li et al., 2018), and biffusion-based decoders (Lin et al., 2022; Yuan et al., 2023) have all been
Due to its recursive definition, ADDTHIN inserts and subsequently deletes some noise events during sampling, which results in additional edit operations compared to PSDIFF.

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proposed. While expressive, autoregressive TPPs are inherently sequential, which makes sampling scale at least linearly with sequence length, can lead to error accumulation in multi-step forecasting and limit conditional generation to forecasting.
Non-autoregressive Neural TPPs: Similar to our method, these approaches model event sequences through a latent variable process that refines the entire sequence jointly. Iiffusion-inspieee (Lüdke et al., 2023; 2025) and flow-based generative models (Kerrigan et al., 2025) have recently emerged as promising alternatives auto-regressive TPP models by directly modelling the joint distribution over event sequences.
CONCLUSION
We have presented EDITPP, an Edit Flow for TPPs that generalises diffusion-based set interpolation methods (Lüdke al., 2023; 2025) with continuous-time flow model introducing substitution as an additional edit operation. By parameterizing insertions, deletions, and substitutions within CTMC, our approach enables efficient and flexible sequence modeling for TPPs. Empirical results demonstrate that EDITPP matches state-of-thee performance in both unconditional and conditional generation tasks across synthetic and real-world datasets, while reducing the number of edit operations.
ACKNOWLEDGMENTS
We want to thank the Munich Center for Machine Learning for providing compute resources.
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A
MODEL PARAMETERS
Table 5: Hyperparameters of our u xz) model shared across all datasets.
Parameter
Value
Number of ins bins bins
64
Number sub bins bub 64
Maximum sub distance å
T/100
Maximum log-rate Am
32
K(8)
1 - cos (5
Llama architecture:
Hidden size H
64
Layers
2
Attention heads
4
Optimizer
Adam 100
Sample steps
All MLPs have input and output sizes of H, except for the final MLP whose output size is determined by the number of and Q parameters the rate. The MLPs have single hidden layer of size 4H. The sinusoidal embeddings map scalar s E [0, 1] to a vector of length H. In contrast to Havasi et al. (2025), we choose cosine к schedule n(s)
cos (z proposed by Nichol & Dhariwal (2021) for diffusion models as it improved results slightly compared (s)) =²
For evaluation, we use exponential moving average (EMA) of the model weights. We also use low-discrepancy sampling of 8 Eq. (14) during training to smooth the loss and thus training signal (Kingma et al., 2023; Lienen et al., 2025).
We train all models for 000 steps and select the best checkpoint by its Wi-over-dEET, which we evaluate validation set every 1000 steps.
B DATA
B.
SYNTHETIC DATASETS
The six synthetic datasets were generated by Shchur et al. (2020b) following the simulation procedures detailed in Section 4.1 of Omi et al. (2019). Each dataset contains 1,000 sequences supported on the interval T
[0, 100). They cover a diverse set of temporal dynamics, defined as follows:
Hawkes Processes (HI, H2). Hawkes processes capture self-exciting features of temporal point processes. The two Hawkes processes are parameterized as follows:
M
X(1 H.) +
Σ
Σ
41).
Getj=l
with H1 (M 1, p, p- 0.2, 01 0.8, 31 1.0) and H2 (M 2, p 0.2, a 0.4, 8, 1.0,
02 = 0.4, 32 20..0..
Non-stationary Poisson Process (NSP). periodic time-varying intensity:
2tt 20000
X(t H4) 0.99 sin
Stationary Renewal Process (SR). Inter-event times T; distribution (mean 1.0, std. 6.0): this produces bursty patterns with short activity bursts followed by long silent periods.
t,+1 are i.i.d. from log- normal
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Table 6: Summary statistics for all synthetic and real-world datasets. the average inter-event time.
Full Name
Abbrev.
# Seq.
Mean Len.
Support [0, T]
T
Hawkes 1
H1
1000
95.4
100
1.01 + 2.38
Hawkes
H2
1000
97.2
100
0.98 + 2.56
Nonstationary Poisson
NSP
1000
100.3
100
0.99 2.22
Nonstationary Renewal
NSR
1000
98.0
100
0.98 1.83
Self- Seff-Correcting
SC
1000
100.2
100
0.99 = 0.71
Stationary Renewal
SR
1000
109.2
100
0.83 + 2.76
PUBG
PG
3001
76.5
38 minutes
0,41 + 0.56
Reddit Comments
R/C
1356
295.7
24 hours
0.07 = 0.28
Reddit Submissions
R/P
1094
1129.0
24 hours
0.02 + 0.03
Taxi Pick-ups (Manhattan)
Tx
182
98.4
24 hours
0.24 + 0.40
Twitter Activity
Tw
2019
14.9
24 hours
1.26 + 2.80
Yelp Check-ins (Airport)
Y/A
319
30.5
24 hours
0.77 1.10
Yelp Check-ins (Mississauga)
Y/M
319
55.2
24 hours
0.43 + 0.96
Non-stationary Renewal Process (NSR). A stationary renewal process is first generated using a gamma distribution (mean 1.0, std. 0.5), then timestamps are time-warped by
2tt
4= r(s) ds,
r(t) 0.99 sin
+
20000
This induces temporally varying expected inter-event intervals while preserving local correlations.
Self-correcting Process (SC). The intensity grows with the time elapsed since the last event:
X(t H4) exp t
Σn Nitt
This discourages extended silent periods and promotes regular spacing.
B.2 REAL-WORLL DATASETS
We use the seven real-world datasets proposed by (Shchur et al., 2020b):
PG (PUBG) represents death-event timestamps from matches of PUBG. R/C (Reddit-Comments) consists of comment timestamps within the first 24 hours threads posted on x/ askscience covering 01. 01.00.122 00.2018-31.112.019 R/P (Reddit-Submission) captures daily submission timestamps from r/polit it ics, covering 01.01.2017-31 1..17-31.12..019.. Tx (Taxi) are taxi pick-up events in the southern part of Manhattan, New York. Tw (Twitter) covers tweet timestamps of ID 25073877, collected over multiple years. Y/A (Yelp-Airport) consists of check-in events at McCarran Inter- national Airport (27 users, year 2018). Lastly. Y/M (Yelp-Mississuuaa) presents check-in for businesses in the city of Mississauga (27 users, year 2018).
C METRICS
standard way in generative modeling to compare generated and real data is the Wasserstein distance (Heusel al., 2017). It is the minimum average distance between elements of the two datasets under the optimal (partial) assignment between them,
Wx (.(Xx') x²) = min,errxx,x") E(a,a))y [d(xr, at x2')7) 1/2
(19)
where dl is distance that compares elements from the two sets. In the case of sequences of unequal length, one can choose itself as a nested Wasserstein distance (Lienen et al., 2024). Xiao et al. (2017) were the first to design such distance between TPPs. They exploit special case of W,
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for sorted sequences of equal length and assign the remaining events of the longer sequence to pseudo-events at to define
dxiao (x, - > 10(0 10))
Σ |o
(20)
|||1++1
where æ' is assumed to be the longer sequence. dxiso captures a difference in both location and number of events between sequences through its terms.
(Shchur et al., 2020b) propose to compute the MMD between sets based on Gaussian kernel and dxiao. addition, we evaluate the event count distributions via a Wasserstein- distance with respect to difference in event counts Wi.d; where (x,
|||| |'|| Finally, we the distributions of inter-event times between our generated sequences and real sequences in W du i.e., a Wasserstein- I distance of dIeT. dIrt is itself the W2 distance between inter-event times of two sequences and quantifies how adjacent events relate each other to capture more complex patterns.
D ABLATIONS
We ablate the hyperparameters 6, Iis and buu in Figs. 5 to 8.
d
dIS
MMD
0.007-
0.0755
PUBG
0.016
0.006
0.0750
0.014
0.0175
Twitter
0.004
0.0150
0.45
0.0125
0.002
Figure 5: Mean and standard error of d;, dIET and MMD two datasets as we vary the 8 parameter for substitutions.
dis
0.008
0.016
PUBG
0.006
0.07525+
0.012
0.46
0.020
0.004
0.015
0.44
27
29
27
2
27
23
20
29
21
20
Dine
Dins
Dins
Figure 6: Mean and standard error of di, dIEr and MMD on two datasets as we vary the number of insertion bins binc-
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dp
dIBT
0.016
0.007
0.0755
PUBG
0.006
0.014
0.006
0,020
Twitter
0.48
0.004
0.015
2
Daub
Daub
Danb
Figure 7: Mean and standard error of di, dIET and MMD two datasets as vary the number of substitution bins bub.
d2
dis
MMD
PUBG
0.006
0.004
0.006
Twitter
0.004
0.015
0.44
Dins
Beub
Bins
beub
Dins
Deub
Figure 8: Mean and standard error of di, dIET and MMD on two datasets as we vary the number of insertion and substitution bins together.
E DETAILED RESULTS
E. INPAINTING VS. FORECASTING
To demonstrate the flexibility of EDITPP for conditional generation, we evaluate its performance when generating events on the interval [2/3, 2T/3). In the forecasting setting, the model is con- ditioned only on events occurring before 7/3, whereas in the inpainting setting, it is conditioned on both the past (t T/3) and the future > 2T /3). As the results show, providing both past and future context substantially improves the quality of the generated middle segment compared to conditioning on the past alone.
PG
R/C
R/P
Tx
Y/A
Y/M
dsiso
Inpainting
2.22 & 0.04
22.66 0.77
13.13 & 0.35
3.02 + 0.20
1.58 0.03
0.59 + 0.02
1.11 + 0.04 1.13 # 0.05
Forecasting
2.27 # 0.05
25.53 # 1.16
18.09 + 0.81
3.27 = 0.33
1.65 = 0.04
0.63 + 0.03
MRE
Inpainting
0.29 +: 0.01
5.79 + 0.96
0.20 +
0.60 + 0.22
1.96
0.48 + 0.01
0.74 0.11
Forecasting
0.30 0.01
5.07 + 1.13
0.33 + 0.01
0.81 + 0.13
2.05 0.11
0.52 + 0.05
0.78 0.08
dET
Inpuinting
0.39
0.40 + 0.01
0.01 0.00
1.13 0.10
0.80 + 0.05
0.70
Forecasting
0.41
0.44 +
0.02
0.10 0.00
1.18
0.78 + 0.07
0.72
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Hawkes
Hawkes-2
Self Comeccing
PSDIT
ADD
Event times for 200 samples from ground truth data (GT) and each model. Each event sequence is represented as a separate row.
Figure 9:
E.2 PARAMETRIC TPP SAMPLES
To illustrate how well each model captures parametric TPPs, we draw 200 samples for the Hawkes and Self-Correcting processes. Fig. 10, we plot the cumulative count N(t) for each sample, while Fig. 9 shows each event sequence as separate row, directly visualizing the events over time. These visualizations further highlight the strong unconditional sampling performance of EDITPP demonstrated in Table 1.
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Hawkes
Hawkes-2
Self-Comecting
300
300
80
150
150
300
300
0
Eor1P
150
80
300
300
PSDur
150
10
300
300
ADDTIIN
150
150
300
300
IFTPP
154
20
100
10
Figure 10: ((t) for 200 samples from ground truth data (GT) and each model.
E.3 FULL RESULTS
Table Forecasting accuracy up to T measured by dIET-
EDITPP
PSDIFF
ADDTHIN
IFTPP
PUBG
0.400 + 0.002
0.413 + 0.009
0.403 0.010
0.473
Reddit Comments
0,684 + 0.005
0.625 # 0.012
0.693
0.684
Reddit Posts
0.010+0.000
0.009 + 0.000
0.010
0.015
Taxi
0.113 + 0.003
0.113 # 0.001
0.145 0.016
Twitter
1.441 = 0.020
1.487 0.012
+.93
2.187
Yelp Airport
0.497 + 0.009
0.492 # 0.005
0.493 0.013
0.587 # 0.019
Yelp Mississauga
0.272 + 0.003
0.262 + 0.003
0.260 + 0.003
0.388 + 0.024
19

---

Published as a conference paper at ICLR 2026
Table 8: Forecasting accuracy up to T measured by mean relative enror of event counts.
EDITPP
PSDIFF
ADDTHIN
IFTPP
PUBG
0.349 + 0.001
0.339 = 0.008
0.367 + 0.005
3.892 = 0.035
Reddit Comments
3.594 + 0.118
3.260 = 0.268
14.777 + 3,226
Reddit Posts
0.281 = 0.001
0.296 0.006
0,457 = 0.065
0.352
Taxi
1.234 0.036
1.040
0.321
Twitter
2.327 0.042
2.984 2.105
0.246
2.060 = 0.027
Yelp Airport
0.350 + 0.007
0.346 + 0.004
0.347 0.014
0.366 # 0.009
Yelp Mississauga
0.902 0.027
0.920 = 0.033
0.374 0.012
0.392 + 0.012
Table 9: Forecasting accuracy up T measured by dxiao-
EDITPP
PSDIFF
ADDTHIN
IFTPP
PUBG
2.478 0.007
2.400 0.007
2.466 0.024
5,954 0.195
Reddit Comments
34.135 + 0.382
32.467 + 0.534
87.666 + 10.184
7.5010
Reddit Posts
48.776 0.355
47.829 + 1.050
72.754 12.134
63.256 9.695
Taxi
4.464 + 0.088
4.444 + 0.076
4.032 # 0.129
4.744 0.1255
Twitter
2.669 0.022
2.635 0.078
2.802 0.132
2.557
0.055
Yelp Airport
1.524 # 0.013
1.512 + 0.016
1.548 0,026
1.795 0.015
Yelp Mississauga
3,027 + 0.046
3.005 0.046
2.895 0.039
3.040
Table 10: Sample quality as measured by MMD.
EDrTPP
PSDIFF
ADDTHIN
IFTPP
Hawkes-1
0.011 + 0.002
0.033 + 0.009
0.024 + 0.009
0.016 0.002
Hawkes-2
0.012 0.001
0.018 0.006
0.018 + 0.006
0.012 0.001
Nonstationary Poisson
0.017 0.003
0.020 = 0.005
0.035 # 0.011
0.032
Nonstationary Renewal
0.035 0.001
0.059 = 0.006
0.157 # 0.084
0.039 0.007
PUBG
0.014 0.001
0.032 = 0.012
0.046 + 0.025
0.162 =
Reddit Comments
0.008
0.006
0.002
0.007 0.003
Reddit Posts
0.024
0.010 0.002
0.004
0.020 0.007
Self-Correcting
0.077 0.004
0.198 0.002
0.246
0.067 +
Stationary Renewal
0.010 = 0.002
0.024 + 0.005
0.025 0.013
0.012 0.002
Taxi
0.031 = 0.002
0.038 + 0.005
0.050 0.000
Twitter
0.013 = 0.002
0.034 = 0.007
0.026 0.012
Yelp Airport
0.037 + 0.002
0.041 + 0.004
0.118 + 0.036
0.058 0.002
Yelp Mississauga
0.040 0.003
0.034 + 0.007
0.037 + 0.006
0.029 0.002
Table 11: Sample quality measured by W--over-dir.-
EDITPP
PSDIFF
ADDTHIN
IFTPP
Hawkes-1
0.526 0.020
0.865 0.035
0.655 0.081
0.628 + 0,030
Hawkes-2
0.546 0.005
0,038
0.703 #
0.0809
Nonstationary Poisson
0.306
0.003
0.015
0.317
Nonstationary Renewal
0.024
0.016
0.393 0.064
0.229 + 0.027
PUBG
0.075
0.090
0.000
0.303 0.039
Reddit Comments
0.144
0.157 0.006
0.532+0.00
0.176 + 0.008
Reddit Posts
0.006
0.004 + 0.000
0.020 + 0.001
0.007 0.001
Self-Correcting
0.064
0.326 0.003 0.003
0.151 + 0.005
0.065 0.001
Stationary Renewal
0.697#00015
1.281 + 0.049
0.941 0.115
0.714 0.028
Taxi
0.111
0.111 0.001 0.001
0.088 + 0.003
0.174 0.015
Twitter
0.460 + 0.004
0.672 + 0.007
0.545 + 0.024
0.492 + 0.023
Yelp Airport
0.246 1.246+0000 0.002
0.244 = 0.004
0.016
0,318 0.017
Yelp Mississauga
0.226 + 0.003
0.225 + 0.003
0.236 + 0.004
0.276 + 0.017
20

---

Published as a conference paper at ICLR 2026
Table 12: Sample quality as measured by W Wi-over-dh.
EDITPP
PSDIFF
ADDTHIN
IFTPP
Hawkes-1
0.008 0.001
0.027 0.008
0.033 # 0.015
0.020
Hawkes-2
0.007 = 0.001
0.030 = 0.009
0.022 0.014
0.013
Nonstationary Poisson
0.003 0.001
1.000
0.012 0.003
Nonstationary Renewal
0.001 = 0.000
=.013
0.014 0.04
PUBG
0.006 0.000
0.016 0.008
0.295 0.024
Reddit Comments
0.002
0.013 + 0.003
0.370
0.039 0.022
Reddit Posts
0.000
0.025 - 0.003
0.045
0.032
Self Self-Correcting
0.001
0.011 = 0.001
0.023
0.001 0.001
Stationary Renewal
0.002
0.030 0.019
0.022
0.023 0.005
Taxi
0.025
0.028 + 0.004
0.023 0.006
0.029 0.003
Twitter
0.003
0.006 + 0.003
0.015 # 0.008
0.007 0.002
Yelp Airport
0.014 0.002
0.015 0.004
0.060 = 0.021
0.033 + 0.003
Yelp Mississauga
0.017
0.015 = 0.002
0.016 + 0.003
0.025 + 0.006
Table 13: Average number edit operations during unconditional sampling.
EDITPP
PSDIFF
Del
Sub
Ins
Del
HI
55.05 + 28.6
65.93 + 10.5
37.74 10.6
92.58 + 34.3
102.50 + 10.6
H2
63.69
9.66
30.98 +
97.57 38.9
NSP
49.59 7.3
49.6647.1
50.56
100.14
100.16
NSR
4..89
4.22
55.88
97.58
100.51
PG
56.69
19.71
19.96
7..32
40.90
R/C
251.3
8.69
15.38
274.49
24.45
R/P
972.89
0.1
23.74
1109.78 +
24.56 1.5677.4
SC
3.7
34.
66.18&8.6
98.95
99.61 10.2
SR
21..6
11.3
38.00
108.85
101.92 10.9
Tw
1.483
2..64
2.0
14.37 10.3
24.46
Tx
96.62 + 14.4
9.3
17.23
97.69 # 17.4
24.37 4.2
Y/A
6.4
22.6445..0
9.00
30,42
24.30
Y/M
54.81 13.8
17.14
11.37
56.54 15.5
24.45 + 4.9
Mean
137.42
33.08
29.16
173.48
61.04
Total
199.65
234.52
21


Reviews:
[{"review_id": "j4Z6wEOe9y", "reviewer": "Reviewer_6JS9", "summary": "This paper proposes a non-autoregressive approach to model temporal point processes (TPP) based on Edit Flows (Havasi, 2025). The proposed method models the rates of edits (insertion, deletion, substitution) via a CTMC. Additionally, it supports modeling sequences of variable lengths by defining an auxiliary alignment space that avoids a separate classifier to determine the number of events during an observation window $[0,T]$.", "questions": "I do like the idea, so if the authors could help address the following key aspects in addition to clearer experimental results, I would be happy to support the paper:\n1. How did the proposed method adapt the discrete flow in the Edit Flows paper to the continuous variable $t$? More specifically, in line 153, if $n$ goes from 0 to infinity, $t^{(n)}$ could have index 0 and infinity, then how can we have a finite number of events? Could the authors help better explain how the state space is defined, and why it is possible to define the set of _all possible_ padded TPP sequences? What does \"padded\" refer to?\n2. For insertion and substitution, if we use a fixed number of $b_\\text{ins}$ and $b_\\text{sub}$ per dataset, can the method handle event sequences where the inter-arrival time distribution has a large variance? I do not expect the method to work for all scenarios, but it would be great to better understand the strengths and limitations of the method.\n3. For the rate model $u_s^{\\theta}$ the paper says they used a Llama backbone (line 309). Is there any specific reason for this modeling choice in the context of TPP?\n4. If the interpolated $z_s$ needs to be sorted (line 252-253), does the training take longer?\n5. Could the authors elaborate on the \"seven real-world and six synthetic benchmark datasets\", e.g., which version of the datasets did the paper use, what are the parameters for parametric TPPs, and what are the summary statistics for real-world datasets? It would be better to have the details in a self-contained paper. \n6. Would it also be possible to visualize the ground truth and sampled events for some parametric TPPs and compare different methods, e.g., Hawkes processes and self-correcting processes (if I correctly understand the results in Table 1)?\n\nOther comments:\n* $\\epsilon$ and $\\text{f}_{\\text{rm-blanks}}$ are notations in the Edit Flows paper, but not defined in this paper, e.g., it is used in line 231.\n* Figure 4, the metric $d_{W_2}$ is missing.\n* It would be great to clarify the ranking in results, e.g., taking the average of five random seeds, and also add error bounds to Table 3 for the number of edit operations.\n\nTypo:\n* Eq.2: $F(T|\\mathcal{H_t})$ -> $F(T|\\mathcal{H_{t^{(n)}}})$.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "* The TPP notation is clear and consistent throughout the paper, making the math easier to follow.\n* The idea is interesting and novel, especially the design of auxiliary alignment space to support varying lengths of TPPs, which has been one of the key challenges for non-autoregressive approaches.", "weaknesses": "* The idea closely follows the Edit Flows paper for language modeling, from parameterization to writing, e.g., Eq. 9-11 in this paper and Eq. 13-15 in the Edit Flows paper; Eq. 14 in this paper and Eq. 23 in the Edit Flows paper. The main difference between language modeling and TPP is that language modeling uses _discrete_ tokens, while TPPs have _continuous_ timestamps. It is unclear to me how the proposed method handles this. Note that I do not take this as a concern of novelty, but the gap could be better addressed, e.g., there is undefined notation in this paper (borrowed from Edit Flows). Please see more detailed questions below.\n* The experimental section is relatively weak. The dataset details are missing, and the paper only uses abbreviations in the main text. The results are also hard to interpret (i.e., a lot of numbers are in bold/underlined). The main text mentions that the ranking is based on the full results in the appendix, but the full results seem to be mixed.\n* The relationship between this paper and other non-autoregressive neural TPP papers is less clear, and the paper lacks visualizations on parametric TPP to verify the methodology, e.g., Hawkes processes.", "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": "HQeaROvIxS", "reviewer": "Reviewer_BAAf", "summary": "The paper introduces a novel framework for modeling Temporal Point Processes (TPPs) through continuous-time editing operations. \n\nThe paper presents the EDITPP framework, which integrates random set interpolation methods for TPPs with discrete sequence editing flow methods. This combination allows for a more effective modeling of event sequences.\nThe framework parameterizes instantaneous rates of insertion, deletion, and substitution operations within a Continuous-Time Markov Chain (CTMC) framework. This approach significantly reduces the number of editing operations required during the generation process.\nThe experimental results demonstrate that EDITPP achieves state-of-the-art performance on various real-world and synthetic datasets for both unconditional and conditional tasks.\nBy introducing an auxiliary alignment space, the framework can be flexibly applied to tasks of varying complexity, enhancing its versatility in different scenarios.\nOverall, the paper showcases the effectiveness of EDITPP in improving the modeling and generation of event sequences in TPPs.", "questions": "1. Could you provide more detailed guidelines or best practices for hyperparameter tuning? Given that the performance of EDITPP may heavily rely on this aspect, clearer instructions could help practitioners achieve optimal results more efficiently.\n\n2. How does EDITPP perform when applied to datasets that differ significantly from those used in training? Are there any specific limitations observed in terms of generalization?\n\n3. What measures have been taken to ensure the computational efficiency of EDITPP during both training and inference? Are there specific scenarios where the model may struggle with efficiency?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. EDITPP effectively combines random set interpolation methods for Temporal Point Processes (TPPs) with discrete sequence editing flow methods, allowing for a more comprehensive modeling approach.\n2. By parameterizing the instantaneous rates of insertion, deletion, and substitution within a Continuous-Time Markov Chain (CTMC) framework, EDITPP significantly reduces the number of editing operations required during the generation process, enhancing efficiency.\n3. The framework demonstrates state-of-the-art performance on various real-world and synthetic datasets for both unconditional and conditional tasks, showcasing its effectiveness and reliability in practical applications.\n4. The introduction of an auxiliary alignment space allows EDITPP to be flexibly applied to tasks of varying complexity, making it versatile for different modeling scenarios and enhancing its applicability across diverse domains.", "weaknesses": "1. While the framework shows strong performance on specific datasets, its generalization capabilities to unseen data or different domains may be limited, necessitating further validation across a broader range of applications.\n2. Although EDITPP reduces the number of editing operations, the overall computational efficiency during training and inference may still be a concern, especially when dealing with large-scale datasets or real-time applications.", "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": "BK55c4uaD7", "reviewer": "Reviewer_eGXi", "summary": "This paper introduce EDITPP, a new way for modeling temporal point processes (TPPs) using an edit-baesd discrete flow matching approach. The method  not only inserts and deletes events like other models, but also substitutes them. It learns the rates of these edits with a Llama transformer model , and it uses a CTMC framework with a special alignment space to make training possible. \nBecause training directly is intractable , the approach uses an auxiliary variable Z, which is an \"alignment space\". For training, it first samples a noise sequence t_0 and a data sequence t_1 and use the Needleman-Wunsch algorithm to create z_0 and z_1. Then, the model is trained to match the ground-truth edit rates that are defined by this Z alignment path. They test this model on many datasets, both real and synthetic, for tasks like generation and forecasting. It shows that adding the \"substitute\" operation makes the model more efficient, using fewer edits and running faster than old models like PSDIFF. As a result, EDITPP shows very strong state-of-the-art results on most of the tasks", "questions": "1. Is it possible to extend the edit approach to marked TPP data? For example, can the approach be used to model a TPP for each event category which can be used to compose into one marked TPP? This approach follows existing works like neural Hawkes process [a] that model intensity function for each type of event separately. Alternatively, can we introduce another operation that predict or change event category on top of the insertion, substituting, deleting operations to model marked TPP? Extending the work to marked TPP data could significantly improve the novelty and innovation of the work.\n2. Can the approach be adapted to interpolation task in the conditional generation setting? It seems to be a strength of the proposed approach over auto-regressive models like IFTPP.\n\nReferences:\n\na. Mei, Hongyuan, and Jason M. Eisner. \"The neural hawkes process: A neurally self-modulating multivariate point process.\" Advances in neural information processing systems 30 (2017).", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The work demonstrates high-Quality presentation and clarity. It is well-written and effectively uses diagrams to explain its complex methodology.\n2. The evaluation of the work is comprehensive. It considers both synthetic and real-world datasets, and both unconditional generation and conditional forecasting tasks. The model also shows much better improved computational efficiency compared to existing diffusion-based TPP models.\n3. The paper successfully applies edit flows from discrete text to the more complex continuous and ordered TPP space. The solution—using an auxiliary alignment space (Z) and leveraging the Needleman-Wunsch algorithm for alignment to define a tractable training objective —is a necessary adaptation of edit flows for it to be compatible with temporal point process data.", "weaknesses": "1. Despite being a successful application of edit flow to TPP data, the approach lacks substantial methodological innovation and novelty. There's no essential difference between the approach and the original edit flow and the introduction of the Needleman-Wunsch algorithm for alignment is an innovation specific to TPP data.\n2. The evaluation results of EDITPP are weak. For example, in Table 2 for conditional forecasting, EDITPP underperforms the baseline models in the majority of the cases. The author uses bold font to indicate the best performing model and underscore to indicate the second best performing model based on overall ranking in the tables, resulting in multiple bold fonts and underscores in each column. Such presentation of models' overall ranking is redundant, unnecessary and confusing. I strongly advise the author to improve the presentation of Table 2.\n3. The proposed approach cannot handle marked TPP data with event categories.\n4. Please refer to the questions section.", "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": "rzxlXAaGY9", "reviewer": "Reviewer_YiHr", "summary": "This paper introduces EDITPP, an Edit Flow framework tailored to Temporal Point Processes (TPPs). TPPs model sequences of random events in continuous time, where both the timing and number of events are stochastic—making them a natural fit for the Edit Flow paradigm. Although the training and sampling procedures are largely adapted from the original Edit Flow with minimal changes, applying the framework to TPPs requires several non-trivial modifications. In particular, the authors reformulate the three discrete edit operations—insertion, substitution, and deletion—to operate over continuous event times, effectively bridging discrete edit dynamics with continuous temporal domains. A LLaMA-based architecture serves as the backbone, and the model is evaluated on a range of unconditional and conditional event generation tasks.", "questions": "1. The term “element-wise mixture path” used in Section 3.2 is never explicitly defined in the paper. Should we assume it refers to the same element-wise mixture path introduced in the original Edit Flow paper? If so, it would be helpful to clarify this connection explicitly.\n\n2. Table 1 states \"bold is best; underlined second best\", but several bolded values differ numerically (like in row MMD, col R/C: 7.5, 6.5, 8.2). Could the authors clarify the criterion for deciding which results are marked as “best”?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The application of Edit Flow to TPP sounds logical and natural.\n\nThe adaptation of the framework from operating in a discrete token space to modeling continuous event arrival times is novel, technically sound, and demonstrates a meaningful extension of the original methodology.\n\nExperimental evaluation is extensive.", "weaknesses": "> While natural and flexible, this factorization (referring to autoregression) comes with inherent limitations: sampling scales linearly with sequence length, errors can compound in  multi-step generation, and conditional generation is restricted to forecasting tasks.\n\nThe authors claimed the above limitations for autoregressive models but I wonder if the current setup would mitigate these. For example, an autoregression can be understood as (in fact, the Edit Flow authors pointed this out in their paper) all left-to-right insertion operations and in this case, edit based methods don't seem to scale better than AR models wrt sequence length. Clarifications for the other two claims are also needed.\n\nIt would be very helpful if the authors could elaborate on why autoregressive models are not favored in this setting since both the data and the task of modeling temporal event sequences are inherently autoregressive to me (if this intuition is wrong, please point out).", "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)