We present Langevin Predictive Coding (LPC), a novel algorithm for deep generative model learning that builds upon the predictive coding framework of computational neuroscience. By injecting Gaussian noise into the predictive coding inference procedure and incorporating an encoder network initialization, we reframe the approach as an amortized Langevin sampling method for optimizing a tight variational lower bound. To increase robustness to sampling step size, we present a lightweight preconditioning technique inspired by Riemannian Langevin methods and adaptive SGD. We compare LPC against VAEs by training generative models on benchmark datasets; our experiments demonstrate superior sample quality and faster convergence for LPC in a fraction of SGD training iterations, while matching or exceeding VAE performance across key metrics like FID, diversity and coverage.

Backpropagation has rapidly become the workhorse credit assignment algorithm for modern deep learning methods. Recently, modified forms of predictive coding (PC), an algorithm with origins in computational neuroscience, have been shown to result in approximately or exactly equal parameter updates to those under backpropagation. Due to this connection, it has been suggested that PC can act as an alternative to backpropagation with desirable properties that may facilitate implementation in neuromorphic systems. Here, we explore these claims using the different contemporary PC variants proposed in the literature. We obtain time complexity bounds for these PC variants, which we show are lower bounded by backpropagation. We also present key properties of these variants that have implications for neurobiological plausibility and their interpretations, particularly from the perspective of standard PC as a variational Bayes algorithm for latent probabilistic models. Our findings shed new light on the connection between the two learning frameworks and suggest that in its current forms, PC may have more limited potential as a direct replacement of backpropagation than previously envisioned.