# Training Generative Adversarial Networks by Solving Ordinary Differential Equations Source: [Training Generative Adversarial Networks by Solving Ordinary Differential Equations]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:45.617Z Authors: Chongli Qin, Yan Wu, Jost Tobias Springenberg, Andrew Brock, Jeff Donahue, Timothy P. Lillicrap, Pushmeet Kohli Published: 2020-10-28T15:23:49.000Z ## Abstract The instability of Generative Adversarial Network (GAN) training has frequently been attributed to gradient descent. Consequently, recent methods have aimed to tailor the models and training procedures to stabilise the discrete updates. In contrast, we study the continuous-time dynamics induced by GAN training. Both theory and toy experiments suggest that these dynamics are in fact surprisingly stable. From this perspective, we hypothesise that instabilities in training GANs arise from the integration error in discretising the continuous dynamics. We experimentally verify that well-known ODE solvers (such as Runge-Kutta) can stabilise training - when combined with a regulariser that controls the integration error. Our approach represents a radical departure from previous methods which typically use adaptive optimisation and stabilisation techniques that constrain the functional space (e.g. Spectral Normalisation). Evaluation on CIFAR-10 and ImageNet shows that our method outperforms several strong baselines, demonstrating its efficacy. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()