# Capturing Conditional Dependence via Auto-regressive Diffusion Models

arXiv: https://arxiv.org/abs/2504.21314 · HTML: https://mlsanity.com/paper/2504.21314/

## 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 24 of its 24 references that are in the map.
- First posted on arXiv 30 Apr 2025.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [VideoFusion: Decomposed Diffusion Models for High-Quality Video Generation](https://mlsanity.com/paper/2303.08320/) (2023)
- [Photorealistic Video Generation with Diffusion Models](https://mlsanity.com/paper/2312.06662/) (2023)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [How Far is Video Generation from World Model: A Physical Law Perspective](https://mlsanity.com/paper/2411.02385/) (2024)
- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [Autoregressive Speech Synthesis without Vector Quantization](https://mlsanity.com/paper/2407.08551/) (2024)
- [O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions](https://mlsanity.com/paper/2409.18959/) (2024)
- [MarDini: Masked Autoregressive Diffusion for Video Generation at Scale](https://mlsanity.com/paper/2410.20280/) (2024)
- [VAR-CLIP: Text-to-Image Generator with Visual Auto-Regressive Modeling](https://mlsanity.com/paper/2408.01181/) (2024)
- [Provable Acceleration for Diffusion Models under Minimal Assumptions](https://mlsanity.com/paper/2410.23285/) (2024)
- [Reverse Transition Kernel: A Flexible Framework to Accelerate Diffusion Inference](https://mlsanity.com/paper/2405.16387/) (2024)
- [Can Diffusion Models Learn Hidden Inter-Feature Rules Behind Images?](https://mlsanity.com/paper/2502.04725/) (2025)

## Abstract (arXiv)

Diffusion models have demonstrated appealing performance in both image and video generation. However, many works discover that they struggle to capture important, high-level relationships that are present in the real world. For example, they fail to learn physical laws from data, and even fail to understand that the objects in the world exist in a stable fashion. This is due to the fact that important conditional dependence structures are not adequately captured in the vanilla diffusion models. In this work, we initiate an in-depth study on strengthening the diffusion model to capture the conditional dependence structures in the data. In particular, we examine the efficacy of the auto-regressive (AR) diffusion models for such purpose and develop the first theoretical results on the sampling error of AR diffusion models under (possibly) the mildest data assumption. Our theoretical findings indicate that, compared with typical diffusion models, the AR variant produces samples with a reduced gap in approximating the data conditional distribution. On the other hand, the overall inference time of the AR-diffusion models is only moderately larger than that for the vanilla diffusion models, making them still practical for large scale applications. We also provide empirical results showing that when there is clear conditional dependence structure in the data, the AR diffusion models captures such structure, whereas vanilla DDPM fails to do so. On the other hand, when there is no obvious conditional dependence across patches of the data, AR diffusion does not outperform DDPM.