# Parallel and Flexible Sampling from Autoregressive Models via Langevin Dynamics

arXiv: https://arxiv.org/abs/2105.08164 · HTML: https://mlsanity.com/paper/2105.08164/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 62 references that are in the map.
- First posted on arXiv 17 May 2021.

## Builds on (most cited first, 30 of 39)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Image Transformer](https://mlsanity.com/paper/1802.05751/) (2018)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [MelGAN: Generative Adversarial Networks for Conditional Waveform Synthesis](https://mlsanity.com/paper/1910.06711/) (2019)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [WaveGlow: A Flow-based Generative Network for Speech Synthesis](https://mlsanity.com/paper/1811.00002/) (2018)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [SampleRNN: An Unconditional End-to-End Neural Audio Generation Model](https://mlsanity.com/paper/1612.07837/) (2016)
- [Music Source Separation in the Waveform Domain](https://mlsanity.com/paper/1911.13254/) (2019)
- [DeepBach: a Steerable Model for Bach Chorales Generation](https://mlsanity.com/paper/1612.01010/) (2016)
- [ClariNet: Parallel Wave Generation in End-to-End Text-to-Speech](https://mlsanity.com/paper/1807.07281/) (2018)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [RNADE: The real-valued neural autoregressive density-estimator](https://mlsanity.com/paper/1306.0186/) (2013)

## Built on by (most cited first, 19 of 19)

- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [It's Raw! Audio Generation with State-Space Models](https://mlsanity.com/paper/2202.09729/) (2022)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [ShapeFormer: Transformer-based Shape Completion via Sparse Representation](https://mlsanity.com/paper/2201.10326/) (2022)
- [Gradient-Based Constrained Sampling from Language Models](https://mlsanity.com/paper/2205.12558/) (2022)
- [Multi-Source Diffusion Models for Simultaneous Music Generation and Separation](https://mlsanity.com/paper/2302.02257/) (2023)
- [Multimodal Image Synthesis and Editing: The Generative AI Era](https://mlsanity.com/paper/2112.13592/) (2021)
- [Diffusion-based Generative Speech Source Separation](https://mlsanity.com/paper/2210.17327/) (2022)
- [AI-Generated Images as Data Source: The Dawn of Synthetic Era](https://mlsanity.com/paper/2310.01830/) (2023)
- [Simultaneous Music Separation and Generation Using Multi-Track Latent Diffusion Models](https://mlsanity.com/paper/2409.12346/) (2024)
- [Latent Autoregressive Source Separation](https://mlsanity.com/paper/2301.08562/) (2023)
- [Unsupervised Source Separation via Bayesian Inference in the Latent Domain](https://mlsanity.com/paper/2110.05313/) (2021)
- [Efficient and Fast Generative-Based Singing Voice Separation using a Latent Diffusion Model](https://mlsanity.com/paper/2511.20470/) (2025)
- [Autoregressive Generative Modeling with Noise Conditional Maximum Likelihood Estimation](https://mlsanity.com/paper/2210.10715/) (2022)
- [Distribution Preserving Source Separation With Time Frequency Predictive Models](https://mlsanity.com/paper/2303.05896/) (2023)
- [Audio Decoding by Inverse Problem Solving](https://mlsanity.com/paper/2409.07858/) (2024)
- [Improving Music Source Separation with Diffusion and Consistency Refinement](https://mlsanity.com/paper/2412.06965/) (2024)
- [Interpretable ODE-style Generative Diffusion Model via Force Field Construction](https://mlsanity.com/paper/2303.08063/) (2023)
- [Source Separation of Multi-source Raw Music using a Residual Quantized Variational Autoencoder](https://mlsanity.com/paper/2408.07020/) (2024)

## Abstract (arXiv)

This paper introduces an alternative approach to sampling from autoregressive models. Autoregressive models are typically sampled sequentially, according to the transition dynamics defined by the model. Instead, we propose a sampling procedure that initializes a sequence with white noise and follows a Markov chain defined by Langevin dynamics on the global log-likelihood of the sequence. This approach parallelizes the sampling process and generalizes to conditional sampling. Using an autoregressive model as a Bayesian prior, we can steer the output of a generative model using a conditional likelihood or constraints. We apply these techniques to autoregressive models in the visual and audio domains, with competitive results for audio source separation, super-resolution, and inpainting.