Implicit generative models such as GANs have achieved remarkable progress at generating convincing fake images, but how well do they really match the distribution?  Log-likelihood has been used extensively to evaluate generative models whenever it’s convenient to do so, but measuring log-likelihoods for implicit generative models presents computational challenges. Furthermore, in order to obtain a density, one needs to smooth the distribution using a noisy model (typically Gaussian), and this choice is hard to motivate. We take a different approach: viewing log-likelihood as a measure of lossless compression, we instead evaluate the lossy compression rates of the generative model, thereby removing the need for a noise distribution.We show how a single run of annealed importance sampling (AIS) can be used to upper bound the entire rate-distortion curve for an implicit generative model. Interestingly, with a Euclidean distortion metric, this is a nearly identical computation to how one would estimate a single scalar log-likelihood. But the rate-distortion curve gives a more complete picture of the performance of the model. We estimate rate-distortion curves for VAEs, GANs, and adversarial autoencoders, and arrive at insights not obtainable from log-likelihoods alone.