mlsanityData to 7 Oct 2026

Mechanisms of Projective Composition of Diffusion Models

arXiv 2502.04549 ↗First posted 6 Feb 2025cs.LGcited by 13

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We study the theoretical foundations of composition in diffusion models, with a particular focus on out-of-distribution extrapolation and length-generalization. Prior work has shown that composing distributions via linear score combination can achieve promising results, including length-generalization in some cases (Du et al., 2023; Liu et al., 2022). However, our theoretical understanding of how and why such compositions work remains incomplete. In fact, it is not even entirely clear what it means for composition to "work". This paper starts to address these fundamental gaps. We begin by precisely defining one possible desired result of composition, which we call projective composition. Then, we investigate: (1) when linear score combinations provably achieve projective composition, (2) whether reverse-diffusion sampling can generate the desired composition, and (3) the conditions under which composition fails. We connect our theoretical analysis to prior empirical observations where composition has either worked or failed, for reasons that were unclear at the time. Finally, we propose a simple heuristic to help predict the success or failure of new compositions.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 42 of its 58 references that are in the map. First posted on arXiv 6 Feb 2025.

Builds on

42 of 58 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025Decentralized Diffusion Models9 Jan
  2. 2024The Superposition of Diffusion Models Using the Ito Density Estimator23 Dec
  3. 2024Towards a Mechanistic Explanation of Diffusion Model Generalization28 Nov
  4. 2024Compositional Image Decomposition with Diffusion Models27 Jun
  5. 2023Correcting Diffusion Generation through Resampling10 Dec
  6. 2023Analyzing and Improving the Training Dynamics of Diffusion Models5 Dec
  7. 2023Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task13 Oct
  8. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis4 Jul
  9. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC22 Feb
  10. 2022Classifier-Free Diffusion Guidance26 Jul
  11. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  12. 2020Denoising Diffusion Implicit Models6 Oct
1 more
  1. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 29

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,456
  2. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,084
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  5. 2023Adding Conditional Control to Text-to-Image Diffusion Modelscited by 5,466
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
  8. 2016CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoningcited by 1,445
  9. 2022Editing Models with Task Arithmeticcited by 1,076
  10. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,023
  11. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 929
  12. 2022Compositional Visual Generation with Composable Diffusion Modelscited by 619
17 more
  1. 2018Disentangling by Factorisingcited by 614
  2. 2022Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learningcited by 553
  3. 2015DRAW: A Recurrent Neural Network For Image Generationcited by 190
  4. 2023Composing Parameter-Efficient Modules with Arithmetic Operationscited by 155
  5. 2024An analytic theory of creativity in convolutional diffusion modelscited by 103
  6. 2023Compositional Foundation Models for Hierarchical Planningcited by 92
  7. 2019A Wasserstein-type distance in the space of Gaussian Mixture Modelscited by 75
  8. 2021Learning to Compose Visual Relationscited by 72
  9. 2021Controllable and Compositional Generation with Latent-Space Energy-Based Modelscited by 64
  10. 2023Compositional Generalization from First Principlescited by 62
  11. 2023Concept Algebra for (Score-Based) Text-Controlled Generative Modelscited by 59
  12. 2023Compositional Diffusion-Based Continuous Constraint Solverscited by 39
  13. 2024Emergence of Hidden Capabilities: Exploring Learning Dynamics in Concept Spacecited by 33
  14. 2023Probabilistic Adaptation of Text-to-Video Modelscited by 29
  15. 2020Compositional Visual Generation and Inference with Energy Based Modelscited by 25
  16. 2023Slot-VAE: Object-Centric Scene Generation with Slot Attentioncited by 20
  17. 2024Compositional Generative Inverse Designcited by 20

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 7; 2026: 6.

13 papers.

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  1. 2025Generative Trajectory Stitching through Diffusion Compositioncited by 38
  2. 2025Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlocited by 18
  3. 2025Efficient Flow Matching using Latent Variablescited by 6
  4. 2025Product of Experts for Visual Generationcited by 6
  5. 2025Local Mechanisms of Compositional Generalization in Conditional Diffusioncited by 3
  6. 2026A Unified Density Operator View of Flow Control and Mergingcited by 2
  7. 2026Compositional Visual Planning via Inference-Time Diffusion Scalingcited by 2
  8. 2025Ctrl-VI: Controllable Video Synthesis via Variational Inferencecited by 1
  9. 2026Long-Text-to-Image Generation via Compositional Prompt Decompositioncited by 1
  10. 2026Scaling Properties of Continuous Diffusion Spoken Language Modelscited by 1
  11. 2026Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolatecited by 1
  12. 2025ScoreMix: Synthetic Data Generation by Score Composition in Diffusion Models Improves Recognitioncited by 0
1 more
  1. 2026Compositional Generalization in Autoregressive Models via Logit Compositioncited by 0

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  1. 2025Loss Functions in Diffusion Models: A Comparative Study
  2. 2026Test-Time Compositional Generalization in Diffusion Models via Concept Discovery
  3. 2026From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models
  4. 2023On the Generalization Properties of Diffusion Models
  5. 2025Generative diffusion models from a PDE perspective
  6. 2025CoInD: Enabling Logical Compositions in Diffusion Models
  7. 2026Rethinking the Diffusion Model from a Langevin Perspective
  8. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models