Edit-Based Flow Matching for Temporal Point Processes

TL;DR

This work introduces EdiTPP, a continuous-time Edit Flow framework for Temporal Point Processes that transports noise sequences to data sequences via insertions, deletions, and substitutions. By parameterizing instantaneous edit rates in a continuous-time Markov process and employing an auxiliary alignment space, EdiTPP enables efficient, non-autoregressive generation with adaptable complexity for both unconditional and conditional tasks. The approach unifies diffusion-like set interpolation with edit-based sequence modeling, achieving state-of-the-art performance across multiple real-world and synthetic datasets while reducing the number of required edits and enabling fast sampling. The method provides a practical, scalable alternative to autoregressive TPP models, with strong forecasting capabilities and tunable trade-offs between speed and fidelity for real-world sequence generation.

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.

Figures (5)

• Figure 1: Edit process transporting ${\bm{t}}_0\sim p_{\text{noise}}({\bm{t}})$ to ${\bm{t}}_1\sim q_{\text{target}}({\bm{t}})$ by inserting, deleting and substituting events.
• Figure 2: Our discrete edit operations transform continuous event sequences through insertions, substitutions and deletion.
• Figure 3: Illustration of the alignment space for ${\bm{t}}_0$ and ${\bm{t}}_1$.
• Figure 4: Changing the number of steps $k$ allows trading off compute and sample quality in terms of $d_{l}$, $d_{W_2}$ and $d_{\mathrm{IET}}$ at inference time.
• Figure : Conditional Sampling