# Feature Likelihood Divergence: Evaluating the Generalization of Generative Models Using Samples

arXiv: https://arxiv.org/abs/2302.04440 · HTML: https://mlsanity.com/paper/2302.04440/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 46 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 30 of 32)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning](https://mlsanity.com/paper/1702.07464/) (2017)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [An empirical study on evaluation metrics of generative adversarial networks](https://mlsanity.com/paper/1806.07755/) (2018)
- [On Memorization in Probabilistic Deep Generative Models](https://mlsanity.com/paper/2106.03216/) (2021)
- [A Non-Parametric Test to Detect Data-Copying in Generative Models](https://mlsanity.com/paper/2004.05675/) (2020)
- [Detecting Overfitting of Deep Generative Networks via Latent Recovery](https://mlsanity.com/paper/1901.03396/) (2019)
- [On the Quantitative Analysis of Decoder-Based Generative Models](https://mlsanity.com/paper/1611.04273/) (2016)
- [Perfect density models cannot guarantee anomaly detection](https://mlsanity.com/paper/2012.03808/) (2020)
- [Protein sequence design with deep generative models](https://mlsanity.com/paper/2104.04457/) (2021)
- [Towards GAN Benchmarks Which Require Generalization](https://mlsanity.com/paper/2001.03653/) (2020)
- [On Training Sample Memorization: Lessons from Benchmarking Generative Modeling with a Large-scale Competition](https://mlsanity.com/paper/2106.03062/) (2021)

## Built on by (most cited first, 25 of 25)

- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction](https://mlsanity.com/paper/2410.08134/) (2024)
- [Be More Diverse than the Most Diverse: Optimal Mixtures of Generative Models via Mixture-UCB Bandit Algorithms](https://mlsanity.com/paper/2412.17622/) (2024)
- [Metrics that matter: Evaluating image quality metrics for medical image generation](https://mlsanity.com/paper/2505.07175/) (2025)
- [Replication in Visual Diffusion Models: A Survey and Outlook](https://mlsanity.com/paper/2408.00001/) (2024)
- [DPImageBench: A Unified Benchmark for Differentially Private Image Synthesis](https://mlsanity.com/paper/2503.14681/) (2025)
- [Consistent Distributed Ranking of Generative Models via Kernel Distances](https://mlsanity.com/paper/2310.11714/) (2023)
- [A Pragmatic Note on Evaluating Generative Models with Fr'echet Inception Distance for Retinal Image Synthesis](https://mlsanity.com/paper/2502.17160/) (2025)
- [Semantic and Visual Crop-Guided Diffusion Models for Heterogeneous Tissue Synthesis in Histopathology](https://mlsanity.com/paper/2509.17847/) (2025)
- [PolyGraph Discrepancy: a classifier-based metric for graph generation](https://mlsanity.com/paper/2510.06122/) (2025)
- [Exposing Diversity Bias in Deep Generative Models: Statistical Origins and Correction of Diversity Error](https://mlsanity.com/paper/2602.14682/) (2026)
- [Statistical Inference for Generative Model Comparison](https://mlsanity.com/paper/2501.18897/) (2025)
- [The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis](https://mlsanity.com/paper/2506.11378/) (2025)
- [Enhanced Generative Model Evaluation with Clipped Density and Coverage](https://mlsanity.com/paper/2507.01761/) (2025)
- [PRIVET: PRoximIty leakage detection Via Extreme value Theory](https://mlsanity.com/paper/2510.24233/) (2025)
- [DSFedMed: Dual-Scale Federated Medical Image Segmentation via Mutual Distillation Between Foundation and Lightweight Models](https://mlsanity.com/paper/2601.16073/) (2026)
- [CytoSyn: a Foundation Diffusion Model for Histopathology -- Tech Report](https://mlsanity.com/paper/2603.18089/) (2026)
- [Mixture-Greedy for Online Generative Model Selection: Is UCB Necessary in Diversity-Aware Multi-Armed Bandits?](https://mlsanity.com/paper/2603.21716/) (2026)
- [Implicit Dynamical Flow Fusion (IDFF) for Generative Modeling](https://mlsanity.com/paper/2409.14599/) (2024)
- [Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesis](https://mlsanity.com/paper/2506.21731/) (2025)
- [From Easy to Hard++: Promoting Differentially Private Image Synthesis Through Spatial-Frequency Curriculum](https://mlsanity.com/paper/2601.06368/) (2026)
- [Do Generative Metrics Predict YOLO Performance? An Evaluation Across Models, Augmentation Ratios, and Dataset Complexity](https://mlsanity.com/paper/2602.18525/) (2026)
- [Fidelity-Diversity Metrics for Text](https://mlsanity.com/paper/2607.04563/) (2026)
- [RA-ClipScore: Making Generative Model Evaluation More Interpretable](https://mlsanity.com/paper/2608.12088/) (2026)
- [PTED: A multi-dimensional two-sample test for scientific inference and generative machine learning](https://mlsanity.com/paper/2609.38388/) (2026)

## Abstract (arXiv)

The past few years have seen impressive progress in the development of deep generative models capable of producing high-dimensional, complex, and photo-realistic data. However, current methods for evaluating such models remain incomplete: standard likelihood-based metrics do not always apply and rarely correlate with perceptual fidelity, while sample-based metrics, such as FID, are insensitive to overfitting, i.e., inability to generalize beyond the training set. To address these limitations, we propose a new metric called the Feature Likelihood Divergence (FLD), a parametric sample-based metric that uses density estimation to provide a comprehensive trichotomic evaluation accounting for novelty (i.e., different from the training samples), fidelity, and diversity of generated samples. We empirically demonstrate the ability of FLD to identify overfitting problem cases, even when previously proposed metrics fail. We also extensively evaluate FLD on various image datasets and model classes, demonstrating its ability to match intuitions of previous metrics like FID while offering a more comprehensive evaluation of generative models. Code is available at https://github.com/marcojira/fld.