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Interacting Diffusion Processes for Event Sequence Forecasting
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Proposes CDiff, a cross-diffusion model with coupled continuous (Gaussian, on Box-Cox-transformed inter-arrival times) and categorical diffusion processes that jointly generate the next N events for long-horizon temporal point process forecasting.
Problem
Forecasting long horizons of event sequences in temporal point processes, where autoregressive models accumulate error and treat event types and inter-arrival times as conditionally independent.
Approach
Two interacting denoising diffusion processes (one Gaussian for Box-Cox transformed inter-arrival times, one categorical for event types) whose denoising networks condition on each other's intermediate states, so the full N-event sequence is generated jointly rather than autoregressively.
Key results
- CDiff achieves best OTD on Taxi (21.013 vs HYPRO 21.653) and Amazon (37.728 vs HYPRO 38.613), and best sMAPE on Taobao (125.685 vs 127.436 LNM) and Taxi (87.993 vs 90.596 TCDDM).
- Ablation: CDiff-indep (no cross-conditioning) is consistently worse than CDiff, e.g. Amazon OTD 40.49 vs 37.73.
- Sampling time is lower than most baselines (e.g. 0.104 s/sequence on Taxi vs 0.265 for HYPRO), except LNM, which is faster.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| jointly model event types and inter-arrival times through interacting denoising processes rather than independent processes (ablation) | CDiff · Amazon | OTD: 40.49 $\pm$ 0.60 -> 37.73 ± 0.20 | Helped |
| jointly model event types and inter-arrival times through interacting denoising processes rather than independent processes (ablation) | CDiff · StackOverflow | RMSE_x+: 1.26 $\pm$ 0.01 -> 1.20 $\pm$ 0.01 | Helped |
| use 25 diffusion steps instead of the selected step count (ablation) | CDiff · StackOverflow | OTD: 41.245 $\pm$ 1.400 -> 42.742 $\pm$ 0.146 | Hurt |
| use 50 diffusion steps instead of 100 (ablation) | CDiff · Taxi | OTD: 21.013 $\pm$ 0.158 -> 21.045 $\pm$ 0.228 | No clear effect |
| use 200 diffusion steps instead of 100 (ablation) | CDiff · Taxi | OTD: 21.013 $\pm$ 0.158 -> 21.545 $\pm$ 0.314 | Hurt |
| use 500 diffusion steps instead of 100 (ablation) | CDiff · Taxi | OTD: 21.013 $\pm$ 0.158 -> 22.107 $\pm$ 0.244 | Hurt |
| add two future-event inference heads (ablation) | AttNHP · Taxi | OTD: 24.762 ± 0.217 -> 26.376$\pm$ 0.229 | Hurt |
| increase parameter count to match CDiff (ablation) | AttNHP · Taxi | OTD: 24.762 ± 0.217 -> 24.174$\pm$ 0.245 | No clear effect |
| use interacting diffusion instead of HYPRO | CDiff · Taxi | OTD: 21.653 ± 0.163 -> 21.013 ± 0.158 | Helped |
| use interacting diffusion instead of HYPRO | CDiff · Taobao | RMSE_e: 2.710 $\pm$ 0.021 -> 2.653 $\pm$ 0.022 | Helped |
| use interacting diffusion instead of the strongest baseline | CDiff · Retweet | OTD: 60.501 ± 0.087 -> 60.661 ± 0.101 | Hurt |
Surprising findings
- Adding extra prediction heads to AttNHP (AttNHP-3) hurts performance rather than helping.
- CDiff has about 1.5x more parameters than baselines on most datasets, but the paper argues that increasing baseline parameters does not close the gap.
Limitations
- Requires a fixed number of events N to be chosen, which is problematic for highly irregular inter-arrival times spanning varying durations.
- Larger parameter count (about 1.5x) than most baselines on most datasets.
Experimental setup
Datasets: Taobao Taxi StackOverflow Retweet MOOC Amazon Synthetic Hawkes
Benchmarks: Taobao Taxi StackOverflow Retweet MOOC Amazon
Metrics: OTD RMSE_e RMSE_x+ sMAPE MAPE MAE_|s| RMSE_|s|
Baselines: Homogeneous Poisson Process NHP AttNHP LNM TCDDM Dual-TPP HYPRO Add-and-thin-augm.
Builds on: denoising diffusion probabilistic models AttNHP Add-and-thin TCDDM
Closest papers by meaning
- EasyTPP: Towards Open Benchmarking Temporal Point Processes (ICLR 2024 · similarity 0.89)
- Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models (ICLR 2025 · similarity 0.89)
- Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations (ICLR 2024 · similarity 0.88)
- Neural Jump-Diffusion Temporal Point Processes (ICML 2024 · similarity 0.88)
- TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation (ICML 2025 · similarity 0.87)
- Deep Continuous-Time State-Space Models for Marked Event Sequences (NeurIPS 2025 · similarity 0.87)
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