Different ways of conditioned on data

[Jice]

Hi everyone,

I have been using BayesFlow 1.0 and 2.0 in my work, and they have performed very well for my studies. Recently, I started revisiting how generative models actually incorporate conditioning on data/observations.

In conditional INNs, we typically concatenate or inject the observed data into the affine coupling layers that map between parameters and latent variables. However, I noticed that there are two other conditioning strategies—such as augmented latent spaces and latent-mixture INNs (shown in the screenshot on the left and middle).

I have been trying to understand the differences among these three conditioning mechanisms, as well as when and why one should use each approach. Unfortunately, I have not been able to find references or papers that specifically discuss augmented latent-space conditioning or latent-mixture INNs.

Does anyone know of relevant references, papers, or implementations that explore these two conditioning schemes?

Thanks in advance!

[KLDivergence]

Hi Jice, bayesflow uses the third approach (SBI). The first approach is suitable when y (observables) have a lower-dimensionality than x (hidden). You can read more about it in the seminal paper by Ardizzone et al. ([1808.04730] Analyzing Inverse Problems with Invertible Neural Networks).

The latent mixture was introduced here: [2001.04872] Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)

For newer works, check out the citing papers.