  Amortized Bayesian inference trains neural networks to solve stochastic
inference problems using model simulations, thereby making it possible to
rapidly perform Bayesian inference for any newly observed data. However,
current simulation-based amortized inference methods are simulation-hungry and
inflexible: They require the specification of a fixed parametric prior,
simulator, and inference tasks ahead of time. Here, we present a new amortized
inference method -- the Simformer -- which overcomes these limitations. By
training a probabilistic diffusion model with transformer architectures, the
Simformer outperforms current state-of-the-art amortized inference approaches
on benchmark tasks and is substantially more flexible: It can be applied to
models with function-valued parameters, it can handle inference scenarios with
missing or unstructured data, and it can sample arbitrary conditionals of the
joint distribution of parameters and data, including both posterior and
likelihood. We showcase the performance and flexibility of the Simformer on
simulators from ecology, epidemiology, and neuroscience, and demonstrate that
it opens up new possibilities and application domains for amortized Bayesian
inference on simulation-based models.
