通过流先验对齐潜在空间

摘要

本文提出了一种新颖的框架，通过利用基于流的生成模型作为先验，将可学习的潜在空间与任意目标分布对齐。我们的方法首先在目标特征上预训练一个流模型，以捕捉其底层分布。随后，这个固定的流模型通过一种对齐损失来正则化潜在空间，该损失重新表述了流匹配目标，将潜在变量视为优化目标。我们正式证明了最小化这种对齐损失，为在目标分布下最大化潜在变量对数似然的变分下界建立了一个计算上可行的替代目标。值得注意的是，所提出的方法消除了计算昂贵的似然评估，并避免了优化过程中的常微分方程求解。作为概念验证，我们在受控环境中展示了对齐损失景观紧密逼近目标分布的负对数似然。我们进一步通过在ImageNet上进行大规模图像生成实验，针对多样化的目标分布验证了方法的有效性，并辅以详细的讨论和消融研究。通过理论和实证的双重验证，我们的框架为潜在空间对齐开辟了一条新途径。

English

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.

通过流先验对齐潜在空间

Aligning Latent Spaces with Flow Priors

摘要

Support