Exploring the Correlation between Likelihood of Flow-based Generative Models and Image Semantics

Among deep generative models, flow-based models, simply referred as \emph{flow}s in this paper, differ from other models in that they provide tractable likelihood. Besides being an evaluation metric of synthesized data, flows are supposed to be robust against out-of-distribution~(OoD) inputs since they do not discard any information of the inputs. However, it has been observed that flows trained on FashionMNIST assign higher likelihoods to OoD samples from MNIST. This counter-intuitive observation raises the concern about the robustness of flows' likelihood. In this paper, we explore the correlation between flows' likelihood and image semantics. We choose two typical flows as the target models: Glow, based on coupling transformations, and pixelCNN, based on autoregressive transformations. Our experiments reveal surprisingly weak correlation between flows' likelihoods and image semantics: the predictive likelihoods of flows can be heavily affected by trivial transformations that keep the image semantics unchanged, which we call semantic-invariant transformations~(SITs). We explore three SITs~(all small pixel-level modifications): image pixel translation, random noise perturbation, latent factors zeroing~(limited to flows using multi-scale architecture, e.g. Glow). These findings, though counter-intuitive, resonate with the fact that the predictive likelihood of a flow is the joint probability of all the image pixels. So flows' likelihoods, modeling on pixel-level intensities, is not able to indicate the existence likelihood of the high-level image semantics. We call for attention that it may be \emph{abuse} if we use the predictive likelihoods of flows for OoD samples detection.