Variational Flow Models: Flowing in Your Style

• URL: http://arxiv.org/abs/2402.02977v4
• Date: Mon, 5 Aug 2024 01:24:52 GMT
• Title: Variational Flow Models: Flowing in Your Style
• Authors: Kien Do, Duc Kieu, Toan Nguyen, Dang Nguyen, Hung Le, Dung Nguyen, Thin Nguyen,
• Abstract summary: We transform the probability flow of a "linear" process into a straight constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation facilitates fast sampling along the original probability flow via the Euler method without training a new model of the SC flow. We can easily integrate high-order numerical solvers into the transformed SC flow, further enhancing the sampling accuracy and efficiency.
• Score: 32.913511518425864
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a systematic training-free method to transform the probability flow of a "linear" stochastic process characterized by the equation X_{t}=a_{t}X_{0}+\sigma_{t}X_{1} into a straight constant-speed (SC) flow, reminiscent of Rectified Flow. This transformation facilitates fast sampling along the original probability flow via the Euler method without training a new model of the SC flow. The flexibility of our approach allows us to extend our transformation to inter-convert two posterior flows of two distinct linear stochastic processes. Moreover, we can easily integrate high-order numerical solvers into the transformed SC flow, further enhancing the sampling accuracy and efficiency. Rigorous theoretical analysis and extensive experimental results substantiate the advantages of our framework. Our code is available at this [https://github.com/clarken92/VFM||link].

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