# Annealed Co-Generation: Disentangling Variables via Progressive Pairwise Modeling

arXiv: https://arxiv.org/abs/2603.06615 · HTML: https://mlsanity.com/paper/2603.06615/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 23 of its 54 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Placed in

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

## Builds on (most cited first, 23 of 23)

- [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)
- [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)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [MultiDiffusion: Fusing Diffusion Paths for Controlled Image Generation](https://mlsanity.com/paper/2302.08113/) (2023)
- [DiGress: Discrete Denoising diffusion for graph generation](https://mlsanity.com/paper/2209.14734/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Collaborative Diffusion for Multi-Modal Face Generation and Editing](https://mlsanity.com/paper/2304.10530/) (2023)
- [DiffCollage: Parallel Generation of Large Content with Diffusion Models](https://mlsanity.com/paper/2303.17076/) (2023)
- [PiFold: Toward effective and efficient protein inverse folding](https://mlsanity.com/paper/2209.12643/) (2022)
- [Conditional Antibody Design as 3D Equivariant Graph Translation](https://mlsanity.com/paper/2208.06073/) (2022)
- [Synthetic Lagrangian Turbulence by Generative Diffusion Models](https://mlsanity.com/paper/2307.08529/) (2023)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Graphically Structured Diffusion Models](https://mlsanity.com/paper/2210.11633/) (2022)
- [Flow Factorized Representation Learning](https://mlsanity.com/paper/2309.13167/) (2023)
- [Diffusion on Graph: Augmentation of Graph Structure for Node Classification](https://mlsanity.com/paper/2503.12563/) (2025)

## Abstract (arXiv)

For multivariate co-generation in scientific applications, we advocate pairwise block rather than joint modeling of all variables. This design mitigates the computational burden and data imbalance. To this end, we propose an Annealed Co-Generation (ACG) framework that replaces high-dimensional diffusion modeling with a low-dimensional diffusion model, which enables multivariate co-generation by composing pairwise variable generations. We first train an unconditional diffusion model over causal variables that are disentangled into pairs. At inference time, we recover the joint distribution by coupling these pairwise models through shared common variables, enabling coherent multivariate generation without any additional training. By employing a three-stage annealing process-Consensus, Heating, and Cooling-our method enforces consistency across shared common variables and progressively constrains each pairwise data distribution to lie on a learnable manifold, while maintaining high likelihood within each pair. We demonstrate the framework's flexibility and efficacy on two distinct scientific tasks: flow-field completion and antibody generation. All datasets and code will be made publicly available upon publication.