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We introduce Sequential Neural Posterior Score Estimation (SNPSE) andSequential Neural Likelihood Score Estimation (SNLSE), two new score-basedmethods for Bayesian inference in simulator-based models. Our methods, inspiredby the success of score-based methods in generative modelling, leverageconditional score-based diffusion models to generate samples from the posteriordistribution of interest. These models can be trained using one of two possibleobjective functions, one of which approximates the score of the intractablelikelihood, while the other directly estimates the score of the posterior. Weembed these models into a sequential training procedure, which guidessimulations using the current approximation of the posterior at the observationof interest, thereby reducing the simulation cost. We validate our methods, aswell as their amortised, non-sequential variants, on several numericalexamples, demonstrating comparable or superior performance to existingstate-of-the-art methods such as Sequential Neural Posterior Estimation (SNPE)and Sequential Neural Likelihood Estimation (SNLE).

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