  Traditional image processing methods employing partial differential equations
(PDEs) offer a multitude of meaningful regularizers, along with valuable
theoretical foundations for a wide range of image-related tasks. This makes
their integration into neural networks a promising avenue. In this paper, we
introduce a novel regularization approach inspired by the reverse process of
PDE-based evolution models. Specifically, we propose inverse evolution layers
(IELs), which serve as bad property amplifiers to penalize neural networks of
which outputs have undesired characteristics. Using IELs, one can achieve
specific regularization objectives and endow neural networks' outputs with
corresponding properties of the PDE models. Our experiments, focusing on
semantic segmentation tasks using heat-diffusion IELs, demonstrate their
effectiveness in mitigating noisy label effects. Additionally, we develop
curve-motion IELs to enforce convex shape regularization in neural
network-based segmentation models for preventing the generation of concave
outputs. Theoretical analysis confirms the efficacy of IELs as an effective
regularization mechanism, particularly in handling training with label issues.
