Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by density estimation performance issues as compared to state-of-the-art autoregressive models. Autoregressive models, which also belong to the family of likelihood-based methods, however suffer from limited parallelizability. In this paper, we propose <italic>Dynamic Linear Flow (DLF)</italic>, a new family of invertible transformations with partially autoregressive structure. Our method benefits from the efficient computation of flow-based methods and high density estimation performance of autoregressive methods. We demonstrate that the proposed DLF yields state-of-the-art performance on ImageNet <inline-formula> <tex-math notation="LaTeX">$32\times 32$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$64\times 64$ </tex-math></inline-formula> out of all flow-based methods. Additionally, DLF converges significantly faster than previous flow-based methods such as Glow.