The paper (arxiv:2103.04689) linked by eutropia above has some empirical evidence on the ML side, showing that performance of predictive coding is not so far off backprop. And there is no shortage of suggestions for how neural circuits might work around the strict requirements of backprop-like algorithms.

cs702's original comment above is excessively hyperbolic: the compositional structure of Bayesian inversion is well known and is known to coincide structurally with the backward/forward structure of automatic differentiation. And there have been many papers before this one showing how predictive coding approximates backprop in other cases, so it is no surprise that it can do so on graphs, too. I agree with the ICLR reviewers that this paper is borderline and not in itself a major contribution. But that does not mean that this whole endeavour, of trying to find explicit mathematical connections between biological and artificial learning, is ill motivated.