# Trans-Dimensional Generative Modeling via Jump Diffusion Models

arXiv: https://arxiv.org/abs/2305.16261 · HTML: https://mlsanity.com/paper/2305.16261/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 25 May 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Model Cards for Model Reporting](https://mlsanity.com/paper/1810.03993/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Flexible Diffusion Modeling of Long Videos](https://mlsanity.com/paper/2205.11495/) (2022)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Equivariant 3D-Conditional Diffusion Models for Molecular Linker Design](https://mlsanity.com/paper/2210.05274/) (2022)
- [Subspace Diffusion Generative Models](https://mlsanity.com/paper/2205.01490/) (2022)
- [From Denoising Diffusions to Denoising Markov Models](https://mlsanity.com/paper/2211.03595/) (2022)
- [Top-N: Equivariant set and graph generation without exchangeability](https://mlsanity.com/paper/2110.02096/) (2021)
- [A Control-Centric Benchmark for Video Prediction](https://mlsanity.com/paper/2304.13723/) (2023)
- [Dimensionality-Varying Diffusion Process](https://mlsanity.com/paper/2211.16032/) (2022)
- [Towards Controllable Diffusion Models via Reward-Guided Exploration](https://mlsanity.com/paper/2304.07132/) (2023)

## Built on by (most cited first, 30 of 35)

- [Pyramidal Flow Matching for Efficient Video Generative Modeling](https://mlsanity.com/paper/2410.05954/) (2024)
- [PixelFlow: Pixel-Space Generative Models with Flow](https://mlsanity.com/paper/2504.07963/) (2025)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [Edit Flows: Flow Matching with Edit Operations](https://mlsanity.com/paper/2506.09018/) (2025)
- [Any-Order Flexible Length Masked Diffusion](https://mlsanity.com/paper/2509.01025/) (2025)
- [Harmonic Self-Conditioned Flow Matching for Multi-Ligand Docking and Binding Site Design](https://mlsanity.com/paper/2310.05764/) (2023)
- [DreamOn: Diffusion Language Models For Code Infilling Beyond Fixed-size Canvas](https://mlsanity.com/paper/2602.01326/) (2026)
- [OneFlow: Concurrent Mixed-Modal and Interleaved Generation with Edit Flows](https://mlsanity.com/paper/2510.03506/) (2025)
- [Multi-domain Distribution Learning for De Novo Drug Design](https://mlsanity.com/paper/2508.17815/) (2025)
- [Insertion Language Models: Sequence Generation with Arbitrary-Position Insertions](https://mlsanity.com/paper/2505.05755/) (2025)
- [Scalable Autoregressive 3D Molecule Generation](https://mlsanity.com/paper/2505.13791/) (2025)
- [A Diffusion Model to Shrink Proteins While Maintaining Their Function](https://mlsanity.com/paper/2511.07390/) (2025)
- [Compositional Flows for 3D Molecule and Synthesis Pathway Co-design](https://mlsanity.com/paper/2504.08051/) (2025)
- [Graph Diffusion that can Insert and Delete](https://mlsanity.com/paper/2506.15725/) (2025)
- [Generative modelling with jump-diffusions](https://mlsanity.com/paper/2503.06558/) (2025)
- [Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions](https://mlsanity.com/paper/2511.09465/) (2025)
- [Pyramidal Patchification Flow for Visual Generation](https://mlsanity.com/paper/2506.23543/) (2025)
- [Spatiotemporal Pyramid Flow Matching for Climate Emulation](https://mlsanity.com/paper/2512.02268/) (2025)
- [PyramidalWan: On Making Pretrained Video Model Pyramidal for Efficient Inference](https://mlsanity.com/paper/2601.04792/) (2026)
- [Equivariant Blurring Diffusion for Hierarchical Molecular Conformer Generation](https://mlsanity.com/paper/2410.20255/) (2024)
- [NEAT: Neighborhood-Guided, Efficient, Autoregressive Set Transformer for 3D Molecular Generation](https://mlsanity.com/paper/2512.05844/) (2025)
- [A Jump-Diffusion Framework for Irregular Time Series Generation](https://mlsanity.com/paper/2505.23215/) (2025)
- [Generative Molecular Morphing for Flexible-Size Design via Unbalanced Optimal Transport](https://mlsanity.com/paper/2606.07239/) (2026)
- [Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion](https://mlsanity.com/paper/2607.10951/) (2026)
- [Variable-Length Generative Protein Design via Generalized Poisson Flow](https://mlsanity.com/paper/2607.09039/) (2026)
- [Discrete Bayesian Sample Inference for Graph Generation](https://mlsanity.com/paper/2511.03015/) (2025)
- [Beyond Two-stage Diffusion TTS: Joint Structure and Content Refinement via Jump Diffusion](https://mlsanity.com/paper/2603.14032/) (2026)
- [Unified Number-Free Text-to-Motion Generation Via Flow Matching](https://mlsanity.com/paper/2603.27040/) (2026)
- [A Continuous-Time Markov Chain Framework for Insertion Language Models](https://mlsanity.com/paper/2606.10199/) (2026)
- [Existence-Field Diffusion Model for Spatial Point Processes with Variable Cardinality](https://mlsanity.com/paper/2607.26428/) (2026)

## Abstract (arXiv)

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately.