ConDiSim: Conditional Diffusion Models for Simulation Based Inference

TL;DR

ConDiSim introduces a conditional diffusion model for simulation-based inference that performs amortized posterior estimation under likelihood-free settings. By forward-diffusing parameters and using a FiLM-conditioned reverse network conditioned on observations, it yields fast, calibrated samples from $p(\boldsymbol{\theta}|\mathbf{y})$, with strong performance on multimodal and high-dimensional posteriors. The method connects to score-based diffusion models in the continuous-time limit and employs classifier-free guidance to balance fidelity and diversity. Across ten benchmarks and two real-world problems, ConDiSim demonstrates competitive accuracy, robustness to noise and distractors, and notably lower training times compared to competing SBI approaches, making it well-suited for fast parameter inference in stochastic simulators with time-series outputs.

Abstract

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions, consisting of a forward process that adds Gaussian noise to parameters, and a reverse process learning to denoise, conditioned on observed data. This approach effectively captures complex dependencies and multi-modalities within posteriors. ConDiSim is evaluated across ten benchmark problems and two real-world test problems, where it demonstrates effective posterior approximation accuracy while maintaining computational efficiency and stability in model training. ConDiSim offers a robust and extensible framework for simulation-based inference, particularly suitable for parameter inference workflows requiring fast inference methods.

Figures (15)

• Figure 1: ConDiSim Architecture: Each diffusion block is FiLM-modulated by timestep and observation embeddings to estimate the noise injected at step $t$ during forward diffusion.
• Figure 2: Two Moons: Comparison of generated and reference posterior distributions, with the ECDF plot representing the cumulative distribution of fractional rank statistics from posterior draws.
• Figure 3: SLCP: Comparison of generated vs. reference posteriors for SLCP and SLCP Distractors.
• Figure 4: Posterior Distributions for Hodgkin–Huxley model.
• Figure 5: Posterior Distributions for Genetic Oscillator model.