# Learning to Jump: Thinning and Thickening Latent Counts for Generative Modeling

arXiv: https://arxiv.org/abs/2305.18375 · HTML: https://mlsanity.com/paper/2305.18375/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 67 of its 88 references that are in the map.
- First posted on arXiv 28 May 2023.

## Builds on (most cited first, 30 of 67)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [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)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)

## Built on by (most cited first, 18 of 18)

- [Add and Thin: Diffusion for Temporal Point Processes](https://mlsanity.com/paper/2311.01139/) (2023)
- [Score Forgetting Distillation: A Swift, Data-Free Method for Machine Unlearning in Diffusion Models](https://mlsanity.com/paper/2409.11219/) (2024)
- [Beta Diffusion](https://mlsanity.com/paper/2309.07867/) (2023)
- [FS-DFM: Fast and Accurate Long Text Generation with Few-Step Diffusion Language Models](https://mlsanity.com/paper/2509.20624/) (2025)
- [Guided Score identity Distillation for Data-Free One-Step Text-to-Image Generation](https://mlsanity.com/paper/2406.01561/) (2024)
- [Advancing Graph Generation through Beta Diffusion](https://mlsanity.com/paper/2406.09357/) (2024)
- [Improving In-Context Learning in Diffusion Models with Visual Context-Modulated Prompts](https://mlsanity.com/paper/2312.01408/) (2023)
- [ItDPDM: Information-Theoretic Discrete Poisson Diffusion Model](https://mlsanity.com/paper/2505.05082/) (2025)
- [Flow Matching for Count Data](https://mlsanity.com/paper/2605.07746/) (2026)
- [Posterior Mean Matching: Generative Modeling through Online Bayesian Inference](https://mlsanity.com/paper/2412.13286/) (2024)
- [Generative Unordered Flow for Set-Structured Data Generation](https://mlsanity.com/paper/2501.17770/) (2025)
- [Dale meets Langevin: A Multiplicative Denoising Diffusion Model](https://mlsanity.com/paper/2510.02730/) (2025)
- [CountsDiff: A Diffusion Model on the Natural Numbers for Generation and Imputation of Count-Based Data](https://mlsanity.com/paper/2604.03779/) (2026)
- [Binomial flows: Denoising and flow matching for discrete ordinal data](https://mlsanity.com/paper/2605.00360/) (2026)
- [CRNDiff: Count-Native Diffusion Framework via Chemical Reaction Networks](https://mlsanity.com/paper/2609.31149/) (2026)
- [One Photon, Many Worlds: Posteriors and Predictions with Single-Photon Cameras](https://mlsanity.com/paper/2610.02675/) (2026)
- [Jumping up and down: Denoiser diffusion models for discrete ordinal data](https://mlsanity.com/paper/2610.02754/) (2026)
- [Mixed Poisson diffusion models and application to posterior sampling](https://mlsanity.com/paper/2610.20218/) (2026)

## Abstract (arXiv)

Learning to denoise has emerged as a prominent paradigm to design state-of-the-art deep generative models for natural images. How to use it to model the distributions of both continuous real-valued data and categorical data has been well studied in recently proposed diffusion models. However, it is found in this paper to have limited ability in modeling some other types of data, such as count and non-negative continuous data, that are often highly sparse, skewed, heavy-tailed, and/or overdispersed. To this end, we propose learning to jump as a general recipe for generative modeling of various types of data. Using a forward count thinning process to construct learning objectives to train a deep neural network, it employs a reverse count thickening process to iteratively refine its generation through that network. We demonstrate when learning to jump is expected to perform comparably to learning to denoise, and when it is expected to perform better. For example, learning to jump is recommended when the training data is non-negative and exhibits strong sparsity, skewness, heavy-tailedness, and/or heterogeneity.