Aligning Latent Spaces with Flow Priors
Authors: name: Yizhuo Li, name: Yuying Ge, name: Yixiao Ge, name: Ying Shan, name: Ping Luo

This paper presents a novel framework for aligning learnable latent spaces to
arbitrary target distributions by leveraging flow-based generative models as
priors. Our method first pretrains a flow model on the target features to
capture the underlying distribution. This fixed flow model subsequently
regularizes the latent space via an alignment loss, which reformulates the flow
matching objective to treat the latents as optimization targets. We formally
prove that minimizing this alignment loss establishes a computationally
tractable surrogate objective for maximizing a variational lower bound on the
log-likelihood of latents under the target distribution. Notably, the proposed
method eliminates computationally expensive likelihood evaluations and avoids
ODE solving during optimization. As a proof of concept, we demonstrate in a
controlled setting that the alignment loss landscape closely approximates the
negative log-likelihood of the target distribution. We further validate the
effectiveness of our approach through large-scale image generation experiments
on ImageNet with diverse target distributions, accompanied by detailed
discussions and ablation studies. With both theoretical and empirical
validation, our framework paves a new way for latent space alignment.