@IssacharNoam Thanks! So basically you compute or approximate the mean and variance on data first conditioned on the c variable, and then use it to construct the GMM prior?

RT @JamesAllingham: Eagerly waiting for #ICLR2025 or #AISTATS2025 results? Are you working on probabilistic #ML, #GenAI, approximate method…

@canaesseth Yes from hierarchical VAE view diffusion models can be viewed as learning a hierarchical prior. But I would like to see if we can learn interesting factorization structure in x like DAGs. This would also be fun in learning dynamic priors for sequence modeling.

@JzinOu @MingtianZhang @xidulu Thanks looks relevant, but mathematically how to extend their hierarchical EBM prior to continuous time case?

@zengqinghong123 Yes one way to resolve the problem re diffusion is to go back to the hierarchical VAE view

@sangwoomo Define “people” in your comment - lot of probabilistic modeling and causal discovery people are crying 🥲

@FrancoisRozet @gil2rok Looks relevant but I would like to use diffusion reverse process or flow as the likelihood/decoder and still learn the prior. Your approach is to learn prior (with diffusion) for a model with fixed likelihood 🤔

@JustusvLiebig Yes causal representation learning is one of the big motivations for me to ask this question 😊

@anirbanray_ It depends on what you want, sure priors that discard info is not perfect for generation, but for representation learning both lossless and lossy compression cases are interesting 😉

@patelmaitreya If you only care about generation from light tail data distributions then go for standard Gaussian indeed. But there are a lot of ways to construct easy-to-sample priors beyond Gaussians with neural networks ☺️

@ChurchillMic Related but not exactly, think about Schrödinger bridges but I would also like to optimize one (or even both) end distributions

@EeroSimoncelli @ZKadkhodaie @FlorentinGuth @StephaneMallat Thanks! I was thinking about learning the prior (ie initial noise distribution) but denoising in fixed basis space is also very interesting. Could you learn the basis then?

@junhong_xu_x I was looking for joint training of the diffusion/flow process and the prior. What do you mean by using RL to learn prior?

@MingtianZhang @xidulu Then I should have asked @JzinOu in the first place before I posted this question on this platform 😂😂😂

@21mb__ @xidulu @_ecunningham_ Yes if you only care about generating nice images then go for Gaussian prior. But I also care about learning non-standard Gaussian prior for structured probabilistic representations.

@xidulu @_ecunningham_ Thanks for the suggestions and I like this paper of using GP prior. But they also choose kernel hyper parameters a priori so technically speaking no prior learning? Also in general how to define continuity equation (of the density form) for stochastic processes?

@bose_joey Yes you are right, the principle is obvious and classic, but I am surprised that at least I haven’t found relevant papers given hundreds of diffusion/flow papers published at ML conf

@bose_joey You are exactly right 👍 if you only care about generation quality, then go for flow matching and you can use any prior. But I also care about prior for structured representations say in a DAG form😉

@h_behjoo I saw this paper in my search -- I believe they pre-fix the GMM prior, so no learning here. See lines 236 - 239. Although can't find any paper doing it, for mixture of DDPM learning I suspect you can combine and

@gil2rok Yes this paper is very nice 👍 but it considers posterior sampling rather than learning generative models. I'd love to see how structured latent variable models can benefit from diffusion/flow-based approaches