Yes, (C1) is a constraint problem. But we also want to satisfy (C2) as close as possible, otherwise we could have just colored some outputs in a single color.
I don't understand about "a single color" unless you mean setting all output pixels to the same color, which would only satisfy the constraints if the input has an NxN patch all one color.
I hope my comment didn't seem to imply that the work seemed unoriginal. I don't think that; I wanted to check my reading.
You understood right, it's constraints + probabilities.
Btw, I have different algorithm that satisfies (C2) perfectly, but not (C1): https://github.com/mxgmn/ConvChain
I might try this approach to generate formal poetry -- it's something I've done by backtracking before, and I'd considered doing something like your ConvChain.
The algorithm used is exactly what you described here. It wasn't obvious to me that probability density functions were not tracked (the algorithm only tracks which NxN patch are allowed at each location) and randomness only come into play when a random valid choice is made, and there each valid patch is chosen probability proportional to its number of occurrence in the input.