Latent diffusion models almost universally place a Gaussian prior on the VAE latent space. For base generation this default is harmless, but under reinforcement‑learning (RL) fine‑tuning it introduces a structural limitation.
The standard VAE’s KL term does not merely ignore mode structure—it actively penalizes separation and tightness. When data are multimodal, the ELBO optimum compresses distinct modes into an overlapping latent region. RL fine‑tuning amplifies this overlap: the score network is under‑resolved on the saddle region between modes, the dynamic‑to‑variational amplification spikes, and the collapse boundary $\beta_c$ is pushed far above its variational scale.
On the real alanine‑dipeptide Boltzmann distribution, a Gaussian‑prior VAE collapses at $\beta_c = 0.224$ while a mode‑tracked Gaussian‑mixture prior collapses at $\beta_c = 0.00316$, a 71× gap. We trace this gap to a single geometric mediator $d_{\min}/(2\sigma_0)$ and verify the causal chain through controlled interventions: moving geometry at fixed prior, and switching prior at matched geometry (full mediation; prior‑label coefficient $0.995\times$, 95% CI $[0.79, 1.25]$).
A three‑source decomposition localises the amplification to the learned policy (zero ODE‑solver contribution, bounded anchor mismatch); the coverage plateau is an unconditional benefit of mode‑separating priors that no amount of RL capacity recovers.
The remedy is conditional: a non‑Gaussian prior is required precisely when the latent geometry would fall into overlap and the task is coverage‑sensitive. A machine‑checked theory skeleton supports the KL pricing structure—a divergent compactness tax under a Gaussian prior versus a finite assignment fee under a mixture—and delineates what is finite‑resource from what necessitates changing the prior.
Review