Compression with Flows via Local Bits-Back Coding
This addresses the problem of efficient lossless compression for users of flow-based generative models, representing an incremental advance by extending coding techniques to a broader model class.
The paper tackles the lack of computationally efficient compression codes for general flow models by introducing local bits-back coding, demonstrating that it closely achieves theoretical codelengths for state-of-the-art flow models on high-dimensional data.
Likelihood-based generative models are the backbones of lossless compression due to the guaranteed existence of codes with lengths close to negative log likelihood. However, there is no guaranteed existence of computationally efficient codes that achieve these lengths, and coding algorithms must be hand-tailored to specific types of generative models to ensure computational efficiency. Such coding algorithms are known for autoregressive models and variational autoencoders, but not for general types of flow models. To fill in this gap, we introduce local bits-back coding, a new compression technique for flow models. We present efficient algorithms that instantiate our technique for many popular types of flows, and we demonstrate that our algorithms closely achieve theoretical codelengths for state-of-the-art flow models on high-dimensional data.