# Learning Stationary Markov Processes with Contrastive Adjustment

arXiv: https://arxiv.org/abs/2303.05497 · HTML: https://mlsanity.com/paper/2303.05497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 25 of 25)

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- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
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- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [LSUN: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop](https://mlsanity.com/paper/1506.03365/) (2015)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Concrete Score Matching: Generalized Score Matching for Discrete Data](https://mlsanity.com/paper/2211.00802/) (2022)
- [Densely connected normalizing flows](https://mlsanity.com/paper/2106.04627/) (2021)
- [Autoregressive Quantile Networks for Generative Modeling](https://mlsanity.com/paper/1806.05575/) (2018)
- [Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net](https://mlsanity.com/paper/1711.02282/) (2017)
- [GSNs : Generative Stochastic Networks](https://mlsanity.com/paper/1503.05571/) (2015)

## Abstract (arXiv)

We introduce a new optimization algorithm, termed contrastive adjustment, for learning Markov transition kernels whose stationary distribution matches the data distribution. Contrastive adjustment is not restricted to a particular family of transition distributions and can be used to model data in both continuous and discrete state spaces. Inspired by recent work on noise-annealed sampling, we propose a particular transition operator, the noise kernel, that can trade mixing speed for sample fidelity. We show that contrastive adjustment is highly valuable in human-computer design processes, as the stationarity of the learned Markov chain enables local exploration of the data manifold and makes it possible to iteratively refine outputs by human feedback. We compare the performance of noise kernels trained with contrastive adjustment to current state-of-the-art generative models and demonstrate promising results on a variety of image synthesis tasks.