# Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning

arXiv: https://arxiv.org/abs/1611.01722 · HTML: https://mlsanity.com/paper/1611.01722/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2016.

## Built on by (most cited first, 21 of 21)

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- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
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- [A Finite-Particle Convergence Rate for Stein Variational Gradient Descent](https://mlsanity.com/paper/2211.09721/) (2022)
- [Particle-based Variational Inference with Preconditioned Functional Gradient Flow](https://mlsanity.com/paper/2211.13954/) (2022)
- [S2AC: Energy-Based Reinforcement Learning with Stein Soft Actor Critic](https://mlsanity.com/paper/2405.00987/) (2024)
- [MonoFlow: Rethinking Divergence GANs via the Perspective of Wasserstein Gradient Flows](https://mlsanity.com/paper/2302.01075/) (2023)
- [Entropy-based Training Methods for Scalable Neural Implicit Sampler](https://mlsanity.com/paper/2306.04952/) (2023)
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- [Emergence of Theory of Mind Collaboration in Multiagent Systems](https://mlsanity.com/paper/2110.00121/) (2021)
- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [Bridging the Gap Between Variational Inference and Wasserstein Gradient Flows](https://mlsanity.com/paper/2310.20090/) (2023)
- [Provably Fast Finite Particle Variants of SVGD via Virtual Particle Stochastic Approximation](https://mlsanity.com/paper/2305.17558/) (2023)
- [Moreau-Yoshida Variational Transport: A General Framework For Solving Regularized Distributional Optimization Problems](https://mlsanity.com/paper/2307.16358/) (2023)
- [Aligning Few-Step Generative Models by Amortizing Sample-based Variational Inference](https://mlsanity.com/paper/2605.26552/) (2026)
- [Reinforcement Learning for Flow-Matching Policies with Density Transport](https://mlsanity.com/paper/2606.08602/) (2026)
- [Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications](https://mlsanity.com/paper/2311.13883/) (2023)
- [Generative Particle Variational Inference via Estimation of Functional Gradients](https://mlsanity.com/paper/2103.01291/) (2021)
- [Denoising Fisher Training For Neural Implicit Samplers](https://mlsanity.com/paper/2411.01453/) (2024)

## Abstract (arXiv)

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output changes along a Stein variational gradient that maximumly decreases the KL divergence with the target distribution. Our method works for any target distribution specified by their unnormalized density function, and can train any black-box architectures that are differentiable in terms of the parameters we want to adapt. As an application of our method, we propose an amortized MLE algorithm for training deep energy model, where a neural sampler is adaptively trained to approximate the likelihood function. Our method mimics an adversarial game between the deep energy model and the neural sampler, and obtains realistic-looking images competitive with the state-of-the-art results.