https://www.chenk.top/en/tags/cnf/Recent content in CNF on Chen Kai BlogHugoenMon, 15 Jul 2024 09:00:00 +0000https://www.chenk.top/en/pde-ml/06-continuous-normalizing-flows/Mon, 15 Jul 2024 09:00:00 +0000https://www.chenk.top/en/pde-ml/06-continuous-normalizing-flows/<p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/en/pde-ml/06-Continuous-Normalizing-Flows/illustration_1.png" alt="PDE and ML (6): Continuous Normalizing Flows and Neural ODE — Chapter overview" loading="lazy" decoding="async" class="content-image"> </figure> </p> <hr> <p>How do you turn an isotropic Gaussian into a photograph of a cat?</p> <p>Normalizing flows give the most direct answer: stack a sequence of invertible transformations and let them push the simple distribution into the complex one. This article&rsquo;s continuous version (CNF) takes that idea to the limit — let the step size go to zero and the discrete chain becomes an ODE. Invertibility is automatic, and the change of density is governed by the instantaneous change of variables formula.</p>