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

翻译：流图模型能够在单次前向传播中实现高质量图像生成。然而，与迭代扩散模型不同，其缺乏显式采样轨迹的特性阻碍了外部约束在条件生成与逆问题求解中的整合。本文提出变分流图，一种将条件采样的视角从"引导采样路径"转变为"学习合适初始噪声"的条件采样框架。具体而言，给定观测数据，我们通过学习噪声适配器模型来输出噪声分布，使得通过流图映射到数据空间后，生成的样本能够同时满足观测约束与数据先验。为此，我们建立了联合训练噪声适配器与流图的变分目标函数，通过提升噪声-数据对齐度，使得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，变分流图能够以单步（或少量）采样生成校准良好的条件样本。在ImageNet数据集上，相较于传统迭代扩散/流模型，变分流图在获得可比拟保真度的同时，实现了数量级级的采样加速。代码已开源：https://github.com/abbasmammadov/VFM