变分流映射：为一步条件生成引入噪声机制

摘要

流映射模型能够通过单次前向传播实现高质量图像生成。然而与迭代式扩散模型不同，其缺乏显式采样轨迹的特性阻碍了外部约束在条件生成和逆问题求解中的集成。我们提出变分流映射（VFM）这一条件采样框架，将条件控制的视角从"引导采样路径"转变为"学习合适的初始噪声"。具体而言，给定观测条件时，我们通过训练噪声适配器模型来输出符合条件约束的噪声分布，使得经过流映射转换到数据空间后的样本既能满足观测约束又保持数据先验特性。为此，我们建立了具有理论依据的变分目标函数，通过联合训练噪声适配器与流映射模型来提升噪声-数据对齐效果，从而仅需简单适配器即可实现复杂数据后验的采样。在多种逆问题上的实验表明，VFM能够通过单次（或少量）迭代生成校准良好的条件样本。在ImageNet数据集上，相较于其他迭代式扩散/流模型，VFM在保持竞争力的生成保真度同时，将采样速度提升了数个数量级。代码发布于https://github.com/abbasmammadov/VFM

English

Flow maps enable high-quality image generation in a single forward pass. However, unlike iterative diffusion models, their lack of an explicit sampling trajectory impedes incorporating external constraints for conditional generation and solving inverse problems. We put forth Variational Flow Maps, a framework for conditional sampling that shifts the perspective of conditioning from "guiding a sampling path", to that of "learning the proper initial noise". Specifically, given an observation, we seek to learn a noise adapter model that outputs a noise distribution, so that after mapping to the data space via flow map, the samples respect the observation and data prior. To this end, we develop a principled variational objective that jointly trains the noise adapter and the flow map, improving noise-data alignment, such that sampling from complex data posterior is achieved with a simple adapter. Experiments on various inverse problems show that VFMs produce well-calibrated conditional samples in a single (or few) steps. For ImageNet, VFM attains competitive fidelity while accelerating the sampling by orders of magnitude compared to alternative iterative diffusion/flow models. Code is available at https://github.com/abbasmammadov/VFM

变分流映射：为一步条件生成引入噪声机制

Variational Flow Maps: Make Some Noise for One-Step Conditional Generation

摘要

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