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Variational Flow Maps (VFMs) are introduced as a framework for conditional image generation with flow maps by learning a noise adapter that outputs a noise distribution conditioned on an observation. A variational objective is used to jointly train the noise adapter and the flow map, improving noise-data alignment for sampling from complex data posteriors. Experiments on inverse problems and ImageNet demonstrate that VFMs produce well-calibrated conditional samples in a single or few steps, achieving competitive fidelity with significantly faster sampling compared to iterative diffusion/flow models.
Ditch the slow sampling dance of diffusion models: Variational Flow Maps let you condition image generation in a single pass by learning the right initial noise.
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