# Logical Guidance for the Exact Composition of Diffusion Models

arXiv: https://arxiv.org/abs/2602.05549 · HTML: https://mlsanity.com/paper/2602.05549/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Compositional Foundation Models for Hierarchical Planning](https://mlsanity.com/paper/2309.08587/) (2023)
- [Multi-LoRA Composition for Image Generation](https://mlsanity.com/paper/2402.16843/) (2024)
- [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)
- [GenMol: A Drug Discovery Generalist with Discrete Diffusion](https://mlsanity.com/paper/2501.06158/) (2025)
- [The Superposition of Diffusion Models Using the Ito Density Estimator](https://mlsanity.com/paper/2412.17762/) (2024)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Compositional Sculpting of Iterative Generative Processes](https://mlsanity.com/paper/2309.16115/) (2023)
- [Diffusion Soup: Model Merging for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2406.08431/) (2024)
- [Compositional 3D-aware Video Generation with LLM Director](https://mlsanity.com/paper/2409.00558/) (2024)
- [Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Design](https://mlsanity.com/paper/2410.20688/) (2024)
- [Tractable Boolean and Arithmetic Circuits](https://mlsanity.com/paper/2202.02942/) (2022)
- [Gradient-Free Classifier Guidance for Diffusion Model Sampling](https://mlsanity.com/paper/2411.15393/) (2024)
- [CoInD: Enabling Logical Compositions in Diffusion Models](https://mlsanity.com/paper/2503.01145/) (2025)

## Built on by (most cited first, 1 of 1)

- [Ensemble-Conditioned Molecular Design](https://mlsanity.com/paper/2609.15077/) (2026)

## Abstract (arXiv)

We propose LOGDIFF (Logical Guidance for the Exact Composition of Diffusion Models), a guidance framework for diffusion models that enables principled constrained generation with complex logical expressions at inference time. We study when exact score-based guidance for complex logical formulas can be obtained from guidance signals associated with atomic properties. First, we derive an exact Boolean calculus that provides a sufficient condition for exact logical guidance. Specifically, if a formula admits a circuit representation in which conjunctions combine conditionally independent subformulas and disjunctions combine subformulas that are either conditionally independent or mutually exclusive, exact logical guidance is achievable. In this case, the guidance signal can be computed exactly from atomic scores and posterior probabilities using an efficient recursive algorithm. Moreover, we show that, for commonly encountered classes of distributions, any desired Boolean formula is compilable into such a circuit representation. Second, by combining atomic guidance scores with posterior probability estimates, we introduce a hybrid guidance approach that bridges classifier guidance and classifier-free guidance, applicable to both compositional logical guidance and standard conditional generation. We demonstrate the effectiveness of our framework on multiple image and protein structure generation tasks.