Title: Heterogeneous Continual Learning. Abstract: We propose a novel framework and a solution to tackle the continual learning (CL) problem with progressive evolution of neural networks. Most CL methods focus on adapting a single network to a new task/class by modifying its weights. However, with rapid progress in architecture design, the problem of adapting existing solutions to novel architectures becomes relevant. For the first time, we propose Heterogeneous Continual Learning (HCL) to address this problem, where a wide range of evolving network architectures emerge continually together with novel data/tasks. As a solution, we build on top of the distillation family of techniques and modify it to a new setting where a weaker model takes the role of a teacher; meanwhile, a new stronger architecture acts as a student. Furthermore, we consider a setup of limited access to previous data and propose Quick Deep Inversion (QDI) to recover prior task visual features to support knowledge transfer. QDI significantly reduces computational costs compared to previous solutions and improves overall performance. In summary, we propose a new setup for CL with a modified knowledge distillation paradigm and design a quick data inversion method to enhance distillation. Our evaluation of various benchmarks shows that the proposed method can successfully progress over various networks while outperforming state-of-the-art methods with a 2x improvement on accuracy.