probabilistic program induction

Can we think about generative flow networks as a potentially tractable formulation of probabilistic program induction?!

executing a line of a program is like an RL action. at every step, there are many possible 'next lines'. generative flow networks would let us learn a policy to write and execute the next line of a program on the fly in such a way that the distribution of sampled traces satisfies some target distribution $R(x)$.

But only to the same extent that regular RL lets us learn a policy to induct optimal programs for an arbitrary reward $R(x)$, which is to say, there's a lot else that has to happen here. We do induct programs pretty well with deep networks and supervised learning.

What about continuous programs? I'm thinking of a literal fluid flow in a high-dimensional space where the coordinates represent a continuous 'computational state' and the actions are local changes to that state, where of course the likelihood of those changes depends on the current state. any given flow represents a 'continuous' probabilistic program, and a flow that achieves consistency with the rewards matches the target distribution.

these are like normalizing flows except that they don't necessarily normalize?