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This method is quite generic for reverse problems so can probably be use to discover some heuristics for SAT problems, or optimization problems, or calibration of ill-defined models. Viewed from afar it's kind of training a global optimizer for your class of problem.
One alternative view is viewing the diffusion model as a degenerate case of RL game, where the reward is greedy (every step gets a reward corresponding to the distance to the solution). The temporal credit assignement is skipped to make the problem easier. To obtain more performance solving the inverse problem as a game with RL should be even better.
On the first run it will train a diffusion model, and save it for subsequent run. (The model is 126M so not sharing it on github and not trained for very long (less than 1hr on a RTX4090) (you can reduce or increase nbiter (number of training iterations) for faster training at the price of less performance ).
It will generate a random state, compute the next state, and then reverse this next state so we know there is at least a solution (not a garden of eden). Have not computed success statistics for but probably > 80% for 10x10 worlds with less than 100 iterations.
