Amortized inference promises fast test-time Bayesian inference, but existing methods typically target a fixed model or a restricted model family. Extending amortization to new model families often requires retraining or test-time fine-tuning. In this paper, we ask: is it possible to build a single inference network capable of generalizing across varying priors, likelihoods, latent dimensions, and observation counts? We introduce Amortized Factor Inference Networks (AFINs), which describe a model as a list of typed prior and likelihood factors and map this description, together with the observations, to a Gaussian posterior approximation through an encode--merge--decode network whose learned parameters do not depend on the latent dimension or the number of observations. Experiments on synthetic and real-data benchmarks show that a single trained AFIN provides competitive posterior approximations at substantially lower test-time cost than NUTS and per-task variational inference. Optional importance sampling can further improve accuracy.

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