# Evaluating Lossy Compression Rates of Deep Generative Models

arXiv: https://arxiv.org/abs/2008.06653 · HTML: https://mlsanity.com/paper/2008.06653/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2020.

## Built on by (most cited first, 16 of 16)

- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Universal Rate-Distortion-Perception Representations for Lossy Compression](https://mlsanity.com/paper/2106.10311/) (2021)
- [Differentiable Annealed Importance Sampling and the Perils of Gradient Noise](https://mlsanity.com/paper/2107.10211/) (2021)
- [MINDE: Mutual Information Neural Diffusion Estimation](https://mlsanity.com/paper/2310.09031/) (2023)
- [On PAC-Bayesian reconstruction guarantees for VAEs](https://mlsanity.com/paper/2202.11455/) (2022)
- [Multi-Rate VAE: Train Once, Get the Full Rate-Distortion Curve](https://mlsanity.com/paper/2212.03905/) (2022)
- [Towards Empirical Sandwich Bounds on the Rate-Distortion Function](https://mlsanity.com/paper/2111.12166/) (2021)
- [Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Coding](https://mlsanity.com/paper/2204.01612/) (2022)
- [Information Theoretic Text-to-Image Alignment](https://mlsanity.com/paper/2405.20759/) (2024)
- [High-dimensional Asymptotics of VAEs: Threshold of Posterior Collapse and Dataset-Size Dependence of Rate-Distortion Curve](https://mlsanity.com/paper/2309.07663/) (2023)
- [Learning multi-modal generative models with permutation-invariant encoders and tighter variational objectives](https://mlsanity.com/paper/2309.00380/) (2023)
- [Generalization in VAE and Diffusion Models: A Unified Information-Theoretic Analysis](https://mlsanity.com/paper/2506.00849/) (2025)
- [INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators](https://mlsanity.com/paper/2502.19183/) (2025)
- [Optimization of Annealed Importance Sampling Hyperparameters](https://mlsanity.com/paper/2209.13226/) (2022)
- [MIST: Mutual Information Estimation Via Supervised Training](https://mlsanity.com/paper/2511.18945/) (2025)
- [Beta-Sigma VAE: Separating beta and decoder variance in Gaussian variational autoencoder](https://mlsanity.com/paper/2409.09361/) (2024)

## Abstract (arXiv)

The field of deep generative modeling has succeeded in producing astonishingly realistic-seeming images and audio, but quantitative evaluation remains a challenge. Log-likelihood is an appealing metric due to its grounding in statistics and information theory, but it can be challenging to estimate for implicit generative models, and scalar-valued metrics give an incomplete picture of a model's quality. In this work, we propose to use rate distortion (RD) curves to evaluate and compare deep generative models. While estimating RD curves is seemingly even more computationally demanding than log-likelihood estimation, we show that we can approximate the entire RD curve using nearly the same computations as were previously used to achieve a single log-likelihood estimate. We evaluate lossy compression rates of VAEs, GANs, and adversarial autoencoders (AAEs) on the MNIST and CIFAR10 datasets. Measuring the entire RD curve gives a more complete picture than scalar-valued metrics, and we arrive at a number of insights not obtainable from log-likelihoods alone.