Aligning Latent Spaces with Flow Priors

2025-06-05

AI Summary

This work addresses the challenge of aligning learnable latent spaces with arbitrary target distributions. We propose a prior-based alignment framework leveraging pretrained normalizing flow models: treating latent variables as optimization parameters, we reconstruct the target distribution via flow matching to derive an efficiently computable alignment loss. To our knowledge, this is the first approach to employ a fixed, pretrained normalizing flow as a distributional prior. We theoretically establish that the proposed loss serves as a valid variational lower bound proxy, circumventing costly likelihood evaluation and ODE solving—thereby substantially improving optimization efficiency. On ImageNet image generation, the alignment loss landscape closely approximates the target negative log-likelihood; ablation studies validate the contribution of each component. Comprehensive theoretical analysis and large-scale experiments jointly demonstrate the framework’s superiority and strong generalization capability.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Aligning learnable latent spaces to target distributions using flow-based priors
• Eliminating expensive likelihood evaluations and ODE solving during optimization
• Validating framework through large-scale image generation on diverse distributions

Innovation

• Leverages flow-based generative models as priors
• Uses alignment loss for latent space regularization
• Eliminates expensive likelihood evaluations and ODE solving