Purrception: Variational Flow Matching for Vector-Quantized Image Generation

2025-10-01

AI Summary

This paper addresses the challenge of jointly optimizing continuous modeling and discrete supervision in vector-quantized (VQ) image generation. We propose the first Variational Flow Matching (VFM) method tailored to VQ latent spaces. Our core innovation lies in learning a velocity field within the continuous embedding space to preserve geometry-aware transport dynamics, while simultaneously incorporating explicit categorical supervision over codebook indices—enabling synergistic optimization of continuous flows and discrete labels. This formulation naturally supports uncertainty quantification and temperature-controlled sampling. On ImageNet-1K at 256×256 resolution, our model converges significantly faster than purely continuous or purely discrete baselines and achieves state-of-the-art FID scores, demonstrating superior efficiency, training stability, and generation quality.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Deep Generative Models & Autoencoders
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We introduce Purrception, a variational flow matching approach for vector-quantized image generation that provides explicit categorical supervision while maintaining continuous transport dynamics. Our method adapts Variational Flow Matching to vector-quantized latents by learning categorical posteriors over codebook indices while computing velocity fields in the continuous embedding space. This combines the geometric awareness of continuous methods with the discrete supervision of categorical approaches, enabling uncertainty quantification over plausible codes and temperature-controlled generation. We evaluate Purrception on ImageNet-1k 256x256 generation. Training converges faster than both continuous flow matching and discrete flow matching baselines while achieving competitive FID scores with state-of-the-art models. This demonstrates that Variational Flow Matching can effectively bridge continuous transport and discrete supervision for improved training efficiency in image generation.

Problem

• Generates vector-quantized images using variational flow matching
• Combines continuous transport dynamics with discrete categorical supervision
• Improves training efficiency while maintaining competitive image quality

Innovation

• Variational flow matching for vector-quantized generation
• Learns categorical posteriors over codebook indices
• Combines continuous transport dynamics with discrete supervision