# The Diffusion Duality, Chapter II: Psi-Samplers

arXiv: https://arxiv.org/abs/2602.21185 · HTML: https://mlsanity.com/paper/2602.21185/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 58 of its 74 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 30 of 58)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [AudioLDM: Text-to-Audio Generation with Latent Diffusion Models](https://mlsanity.com/paper/2301.12503/) (2023)
- [Structure and Content-Guided Video Synthesis with Diffusion Models](https://mlsanity.com/paper/2302.03011/) (2023)
- [A Discourse-Aware Attention Model for Abstractive Summarization of Long Documents](https://mlsanity.com/paper/1804.05685/) (2018)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)

## Built on by (most cited first, 12 of 12)

- [ELF: Embedded Language Flows](https://mlsanity.com/paper/2605.10938/) (2026)
- [How to Train Your Latent Diffusion Language Model Jointly With the Latent Space](https://mlsanity.com/paper/2605.07933/) (2026)
- [Drifting Objectives for Refining Discrete Diffusion Language Models](https://mlsanity.com/paper/2605.19470/) (2026)
- [Simplex Relaxation for Discrete Diffusion](https://mlsanity.com/paper/2608.10615/) (2026)
- [Unlocking Lossless Speedups in LLMs via Discrete Diffusion](https://mlsanity.com/paper/2609.04010/) (2026)
- [From Scores to Gibbs Correctors: Accelerating Uniform-Rate Discrete Diffusion Models](https://mlsanity.com/paper/2605.27352/) (2026)
- [From Truncation to Commitment: Persistent Context in Uniform Discrete Diffusion](https://mlsanity.com/paper/2609.01043/) (2026)
- [Diffusion Language Models for Speech Recognition](https://mlsanity.com/paper/2604.14001/) (2026)
- [BlockGen: Flexible Blockwise Sequence Modeling with Hybrid Samplers](https://mlsanity.com/paper/2606.02241/) (2026)
- [Entropy Can Flow, or It Can Guide. Be Entropy. LEDFlow: Introducing Entropy-guided Generation Order into Uniform Discrete Flow](https://mlsanity.com/paper/2609.25131/) (2026)
- [Simple Diffusion Language Models Are More Effective Few-Step Generators Than Reported](https://mlsanity.com/paper/2609.33947/) (2026)
- [Less Uniform Discrete Diffusion is More Powerful and Scalable](https://mlsanity.com/paper/2609.35817/) (2026)

## Abstract (arXiv)

Uniform-state discrete diffusion models excel at few-step generation and guidance due to their ability to self-correct, making them preferred over autoregressive or Masked diffusion models in these settings. However, their sampling quality plateaus with ancestral samplers as the number of steps increases. We introduce a family of Predictor-Corrector (PC) samplers for discrete diffusion that generalize prior methods and apply to arbitrary noise processes. When paired with uniform-state diffusion, our samplers outperform ancestral sampling on both language and image modeling, achieving lower generative perplexity at matched unigram entropy on OpenWebText and better FID/IS scores on CIFAR10. Crucially, unlike conventional samplers, our PC methods continue to improve with more sampling steps. Taken together, these findings call into question the assumption that Masked diffusion is the inevitable future of diffusion-based language modeling. Beyond sampling, we develop a memory-efficient curriculum for the Gaussian relaxation training phase, reducing training time by 25% and memory by 33% compared to Duo while maintaining comparable perplexity on OpenWebText and LM1B and strong downstream performance. We release code, checkpoints, and a video-tutorial on: https://s-sahoo.com/duo-ch2