# Variational f-divergence Minimization

arXiv: https://arxiv.org/abs/1907.11891 · HTML: https://mlsanity.com/paper/1907.11891/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2019.

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

- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Training Neural Samplers with Reverse Diffusive KL Divergence](https://mlsanity.com/paper/2410.12456/) (2024)
- [Improving Probabilistic Diffusion Models With Optimal Diagonal Covariance Matching](https://mlsanity.com/paper/2406.10808/) (2024)
- [Negating Negatives: Alignment with Human Negative Samples via Distributional Dispreference Optimization](https://mlsanity.com/paper/2403.03419/) (2024)
- [Beyond Squared Error: Exploring Loss Design for Enhanced Training of Generative Flow Networks](https://mlsanity.com/paper/2410.02596/) (2024)
- [DiffRatio: Training One-Step Diffusion Models Without Teacher Supervision](https://mlsanity.com/paper/2502.08005/) (2025)
- [An energy-based deep splitting method for the nonlinear filtering problem](https://mlsanity.com/paper/2203.17153/) (2022)
- [Moment Matching Denoising Gibbs Sampling](https://mlsanity.com/paper/2305.11650/) (2023)
- [Bayesian brains and the R'enyi divergence](https://mlsanity.com/paper/2107.05438/) (2021)
- [Spread Flows for Manifold Modelling](https://mlsanity.com/paper/2109.14216/) (2021)
- [Greedy Bayesian Posterior Approximation with Deep Ensembles](https://mlsanity.com/paper/2105.14275/) (2021)
- [A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel](https://mlsanity.com/paper/2111.10722/) (2021)
- [Importance Weighted Score Matching for Diffusion Samplers with Enhanced Mode Coverage](https://mlsanity.com/paper/2505.19431/) (2025)
- [VarDiU: A Variational Diffusive Upper Bound for One-Step Diffusion Distillation](https://mlsanity.com/paper/2508.20646/) (2025)
- [Neural Posterior Regularization for Likelihood-Free Inference](https://mlsanity.com/paper/2102.07770/) (2021)
- [Empirical Risk Minimization with f-Divergence Regularization](https://mlsanity.com/paper/2601.13191/) (2026)

## Abstract (arXiv)

Probabilistic models are often trained by maximum likelihood, which corresponds to minimizing a specific f-divergence between the model and data distribution. In light of recent successes in training Generative Adversarial Networks, alternative non-likelihood training criteria have been proposed. Whilst not necessarily statistically efficient, these alternatives may better match user requirements such as sharp image generation. A general variational method for training probabilistic latent variable models using maximum likelihood is well established; however, how to train latent variable models using other f-divergences is comparatively unknown. We discuss a variational approach that, when combined with the recently introduced Spread Divergence, can be applied to train a large class of latent variable models using any f-divergence.