# CoInD: Enabling Logical Compositions in Diffusion Models

arXiv: https://arxiv.org/abs/2503.01145 · HTML: https://mlsanity.com/paper/2503.01145/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 26 of its 37 references that are in the map.
- First posted on arXiv 3 Mar 2025.

## Placed in

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

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulation](https://mlsanity.com/paper/2110.02711/) (2021)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [Applying Guidance in a Limited Interval Improves Sample and Distribution Quality in Diffusion Models](https://mlsanity.com/paper/2404.07724/) (2024)
- [Stable Bias: Analyzing Societal Representations in Diffusion Models](https://mlsanity.com/paper/2303.11408/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task](https://mlsanity.com/paper/2310.09336/) (2023)
- [Learning to Compose Visual Relations](https://mlsanity.com/paper/2111.09297/) (2021)
- [Controllable and Compositional Generation with Latent-Space Energy-Based Models](https://mlsanity.com/paper/2110.10873/) (2021)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [Visual Representation Learning Does Not Generalize Strongly Within the Same Domain](https://mlsanity.com/paper/2107.08221/) (2021)
- [Score-based Generative Modeling Secretly Minimizes the Wasserstein Distance](https://mlsanity.com/paper/2212.06359/) (2022)
- [How Diffusion Models Learn to Factorize and Compose](https://mlsanity.com/paper/2408.13256/) (2024)
- [OASIS Uncovers: High-Quality T2I Models, Same Old Stereotypes](https://mlsanity.com/paper/2501.00962/) (2025)
- [Enhanced Controllability of Diffusion Models via Feature Disentanglement and Realism-Enhanced Sampling Methods](https://mlsanity.com/paper/2302.14368/) (2023)

## Built on by (most cited first, 8 of 8)

- [Product of Experts for Visual Generation](https://mlsanity.com/paper/2506.08894/) (2025)
- [SUB: Benchmarking CBM Generalization via Synthetic Attribute Substitutions](https://mlsanity.com/paper/2507.23784/) (2025)
- [What Drives Compositional Generalization in Visual Generative Models? The Importance of Continuous Training Objectives](https://mlsanity.com/paper/2510.03075/) (2025)
- [Factored Diffusion Policies:Compositionally Generalized Robot Control with a Single Score Network](https://mlsanity.com/paper/2605.22596/) (2026)
- [Ctrl-VI: Controllable Video Synthesis via Variational Inference](https://mlsanity.com/paper/2510.07670/) (2025)
- [Logical Guidance for the Exact Composition of Diffusion Models](https://mlsanity.com/paper/2602.05549/) (2026)
- [Assessing Sample Quality in Conditional Generation under Compositional Shift](https://mlsanity.com/paper/2606.09601/) (2026)
- [Compositional Generative Modeling from Decentralized Data](https://mlsanity.com/paper/2606.10153/) (2026)

## Abstract (arXiv)

How can we learn generative models to sample data with arbitrary logical compositions of statistically independent attributes? The prevailing solution is to sample from distributions expressed as a composition of attributes' conditional marginal distributions under the assumption that they are statistically independent. This paper shows that standard conditional diffusion models violate this assumption, even when all attribute compositions are observed during training. And, this violation is significantly more severe when only a subset of the compositions is observed. We propose CoInD to address this problem. It explicitly enforces statistical independence between the conditional marginal distributions by minimizing Fisher's divergence between the joint and marginal distributions. The theoretical advantages of CoInD are reflected in both qualitative and quantitative experiments, demonstrating a significantly more faithful and controlled generation of samples for arbitrary logical compositions of attributes. The benefit is more pronounced for scenarios that current solutions relying on the assumption of conditionally independent marginals struggle with, namely, logical compositions involving the NOT operation and when only a subset of compositions are observed during training.