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Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models

ICML 2024 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Score-based generative modeling analysis

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Proposes score-based diffusion SBI (NPSE) and a truncated sequential variant (TSNPSE) that trains a conditional score network on posterior scores and samples via probability-flow ODE, matching or beating SNPE-type baselines on benchmarks and a pyloric neuroscience model.

Problem

Simulation-based Bayesian inference with intractable likelihoods; existing sequential neural posterior methods rely on normalising flows, and sequential proposals create a mismatch that must be corrected.

Approach

Use a conditional score-based diffusion model trained by denoising posterior score matching to approximate the perturbed posterior score, sample via the reverse SDE or probability flow ODE, and make it sequential with truncated-prior proposals (HPR truncation) so no importance correction is needed.

Key results

• On the two hardest benchmarks, SLCP and Lotka Volterra, the proposed methods outperform competitors per the paper's C2ST results.
• On the pyloric network, TSNPSE reaches 81% valid summary statistics in the final round, reported as superior to other methods at the same budget.
• Results on the other benchmarks are described as mixed, depending on task and budget.

Measured effects reported in the paper

Surprising findings

• Corrections in SNPSE-A, SNPSE-B and SNPSE-C performed significantly worse than the truncated approach, so the paper advocates TSNPSE alone.

Limitations

• CNF sampling and likelihood evaluation are computationally more expensive than normalising-flow TSNPE.
• Simple MLP architecture with limited tuning; no extensive hyperparameter search.
• Performance depends on choice of VE or VP SDE, with no single best choice across tasks.

Experimental setup

Datasets: SBI benchmarks (SLCP, Lotka Volterra, and others) pyloric network simulator data

Benchmarks: SLCP Lotka Volterra eight sbibm benchmark tasks pyloric network

Metrics: C2ST percentage of valid summary statistics

Baselines: NPE SNPE-C TSNPE SNVI FMPE

Builds on: score-based generative modelling SNPE-C TSNPE FMPE probability flow ODE

Closest papers by meaning

• Compositional Score Modeling for Simulation-Based Inference (ICML 2023 · similarity 0.90)
• Truncated proposals for scalable and hassle-free simulation-based inference (NeurIPS 2022 · similarity 0.89)
• Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraints (AAAI 2025 · similarity 0.88)
• Nearest Neighbour Score Estimators for Diffusion Generative Models (ICML 2024 · similarity 0.87)
• Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization (ICLR 2024 · similarity 0.87)
• Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior (ICLR 2025 · similarity 0.86)