A couple more iterations in, this varient defines a time dependent base distribution with a time dependent posterior and prior flow.
Seems like a likely candidate for time dependent vaes, the posterior flow helps a lot in particular. Replacing the decoder in this varient with a time dependent conditional flow seems to give really great temporal consistency without much work.
This formulation is as follows:
maximize_{θ, φ} E_{q_φ(c | x)} [
log p_θ(x | z, t)
+ log p_θ(y | t)
+ log |det J_{f_θ}(z; c, t)|
+ log p_θ(c | t)
- log q_φ(c | x)
];
where
z = enc_θ(x),
y = f_θ(z; c, t),
p_θ(x | z, t) = Bernoulli(σ(g_θ(z, t))).
@misc{algomancer2025,
author = {@algomancer},
title = {Some Dumb Shit},
year = {2025}
}