Causal Time Series Generation via Diffusion Models

TL;DR

This work reframes conditional time series generation as a causal task on Pearl's causal ladder, introducing Obs-TSG, Int-TSG, and CF-TSG. It presents CaTSG, a diffusion-based framework that uses backdoor-adjusted guidance and a latent environment bank to handle unobserved confounding and enable interventional and counterfactual generation. The methodology derives interventional and counterfactual score functions via backdoor adjustment and abduction–action–prediction, and demonstrates improved fidelity and counterfactual capabilities on synthetic and real datasets. The approach offers a promising path toward reliable simulation under interventions and personalized counterfactual generation in time series, with potential impact on policy planning, risk assessment, and decision support.

Abstract

Time series generation (TSG) synthesizes realistic sequences and has achieved remarkable success. Among TSG, conditional models generate sequences given observed covariates, however, such models learn observational correlations without considering unobserved confounding. In this work, we propose a causal perspective on conditional TSG and introduce causal time series generation as a new TSG task family, formalized within Pearl's causal ladder, extending beyond observational generation to include interventional and counterfactual settings. To instantiate these tasks, we develop CaTSG, a unified diffusion-based framework with backdoor-adjusted guidance that causally steers sampling toward desired interventions and individual counterfactuals while preserving observational fidelity. Specifically, our method derives causal score functions via backdoor adjustment and the abduction-action-prediction procedure, thus enabling principled support for all three levels of TSG. Extensive experiments on both synthetic and real-world datasets show that CaTSG achieves superior fidelity and also supporting interventional and counterfactual generation that existing baselines cannot handle. Overall, we propose the causal TSG family and instantiate it with CaTSG, providing an initial proof-of-concept and opening a promising direction toward more reliable simulation under interventions and counterfactual generation.

Figures (13)

• Figure 1: Motivation for causal time series generation. (a) We observe time series $X$ and $C$, (b) yet unobserved factors $E$ may affect both. (c) Standard conditional TSG risk learning spurious correlations. (d) We extend this paradigm into a causal TSG family with Int-TSG and CF-TSG. (e) Three tasks yield distinct outputs given same $C$.
• Figure 2: Structural Causal Models (SCMs) for different conditional time series generation paradigms.
• Figure 3: Overview of CaTSG. (a) Generative objectives for observational, interventional, and counterfactual TSG. (b) Model instantiation: CaTSG consists of EnvInfer, Environment Bank, and Denoiser. Blue variables are used only for $\mathcal{L}_{\text{sw}}$, Env. Bank is regularized by $\mathcal{L}_{\text{orth}}$, and Denoiser is regularized by $\mathcal{L}_{\text{eps}}$. (c) Swapped prediction loss.
• Figure 4: (a) Factual samples $X$ and (b) counterfactual generations $\hat{X}'$ on Traffic. (c) Global distribution over all samples: histogram and ECDF of $X$ (blue) and $\hat{X}'$ (orange).
• Figure 5: (a) Environment posterior $\mathbf{w}$ across splits. (b) t-SNE of representations on Harmonic-VM. Shaded ellipses are one standard-deviation regions. (c) Ablation of components. (d) Hyperparameter sensitivity on Harmonic-VM.