Flowing Backwards: Improving Normalizing Flows via Reverse Representation Alignment

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new samples from this space. This characteristic creates an intrinsic synergy between representation learning and data generation. However, the generative quality of standard NFs is limited by poor semantic representations from log-likelihood optimization. To remedy this, we propose a novel alignment strategy that creatively leverages the invertibility of NFs: instead of regularizing the forward pass, we align the intermediate features of the generative (reverse) pass with representations from a powerful vision foundation model, demonstrating superior effectiveness over naive alignment. We also introduce a novel training-free, test-time optimization algorithm for classification, which provides a more intrinsic evaluation of the NF's embedded semantic knowledge. Comprehensive experiments demonstrate that our approach accelerates the training of NFs by over 3.3$\times$, while simultaneously delivering significant improvements in both generative quality and classification accuracy. New state-of-the-art results for NFs are established on ImageNet 64$\times$64 and 256$\times$256. Our code is available at https://github.com/MCG-NJU/FlowBack.