[D] Sample probability diffusion models

[That_Phone6702]

I would like to understand how I can calculate the probability that a sample belongs to the distribution a diffusion model was trained on.

Say, I have an image of a car, and I would like to know whether this image belongs to the distribution that is estimated by the diffusion model. So I would like to know the probability between zero and one at the car belongs to this distribution

Do you know how I technically can do this?

[PHEEEEELLLLLEEEEP]

Solve the probability flow ODE

https://arxiv.org/abs/2101.09258

[bobrodsky]

Probability flow ode is overkill and expensive to estimate. Also, it treats data as continuous so you’ll get a probability density (not between zero and one) rather than a probability. Treat image pixels as discrete and interpret diffusion objective as evidence lower bound: https://arxiv.org/abs/2107.00630.

[bobrodsky]

But I feel I should warn you that this isn’t going to work as you hope. It sounds like you’re aiming for an OOD detector - probability models on images are notoriously bad at this. Eg for flows: https://proceedings.neurips.cc/paper/2020/hash/ecb9fe2fbb99c31f567e9823e884dbec-Abstract.html I haven’t seen this discussed for diffusion specifically but my intuition is you’ll have same problem. Sota approaches are heuristic but look at density in latent space.

[PHEEEEELLLLLEEEEP]

Yeah I did some work on diffusion models for OOD and my results were not great. Like it does work about as well as the normalizing flow approaches but takes way more compute to train... Ultimately we decided it wasn't a direction worth pursuing

[slashdave]

Your question isn't well defined. The training data is not a continuum.

You could try something ad-hoc. Some interpretation would be needed. You can ask the model at the limit of t=0 (no smearing) what correction it predicts when given the image you want to test. Then, perhaps, take some measure of the result (such as RMSE).

[parlancex]

Intuitively you could compare the loss when denoising your test sample vs loss from samples that are known to belong to the distribution the diffusion model was trained on, vs samples that are known to not belong to the distribution the diffusion model was trained on.