I was considering an unconditional latent diffusion model, but for conditional models, the computation becomes much more complex (we might have to use bayes here). If we use Score-Based Generative Modeling (https://arxiv.org/abs/2011.13456), we could try to find and count all the unique local minima and saddle points, but it is not clear how we can do this...

You don't need to use a single seed for the noise patch, you can use random numbers and it will work just fine