Physics Informed Distillation for Diffusion Models
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
Diffusion models have recently emerged as a potent tool in generative modeling. However, their inherent iterative nature often results in sluggish image generation due to the requirement for multiple model evaluations. Recent progress has unveiled the intrinsic link between diffusion models and Probability Flow Ordinary Differential Equations (ODEs), thus enabling us to conceptualize diffusion models as ODE systems. Simultaneously, Physics Informed Neural Networks (PINNs) have substantiated their effectiveness in solving intricate differential equations through implicit modeling of their solutions. Building upon these foundational insights, we introduce Physics Informed Distillation (PID), which employs a student model to represent the solution of the ODE system corresponding to the teacher diffusion model, akin to the principles employed in PINNs. Through experiments on CIFAR 10 and ImageNet 64x64, we observe that PID achieves performance comparable to recent distillation methods. Notably, it demonstrates predictable trends concerning method-specific hyperparameters and eliminates the need for synthetic dataset generation during the distillation process. Both of which contribute to its easy-to-use nature as a distillation approach for Diffusion Models. Our code and pre-trained checkpoint are publicly available at: https://github.com/pantheon5100/pid_diffusion.git.
Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 40 of its 53 references that are in the map. First posted on arXiv 13 Nov 2024.
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40 of 53 references.
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Other references · 39
- 2020Denoising Diffusion Probabilistic Modelscited by 20,851
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
- 2020Denoising Diffusion Implicit Modelscited by 9,655
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
- 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
- 2023Segment Anythingcited by 8,158
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
- 2021Emerging Properties in Self-Supervised Vision Transformerscited by 6,893
- 2022Hierarchical Text-Conditional Image Generation with CLIP Latentscited by 6,539
- 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
- 2022Generative Adversarial Networkscited by 5,603
27 more
- 2020Bootstrap your own latent: A new approach to self-supervised Learningcited by 4,712
- 2021GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Modelscited by 3,595
- 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
- 2016Improved Techniques for Training GANscited by 2,938
- 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
- 2020Improved Baselines with Momentum Contrastive Learningcited by 2,282
- 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,961
- 2023Consistency Modelscited by 1,778
- 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
- 2021Image Super-Resolution via Iterative Refinementcited by 1,506
- 2019On the Variance of the Adaptive Learning Rate and Beyondcited by 763
- 2022Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's nextcited by 603
- 2022Fast Sampling of Diffusion Models with Exponential Integratorcited by 526
- 2021Label-Efficient Semantic Segmentation with Diffusion Modelscited by 495
- 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 448
- 2021SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Modelscited by 415
- 2021Knowledge Distillation in Iterative Generative Models for Improved Sampling Speedcited by 344
- 2021Deblurring via Stochastic Refinementcited by 248
- 2023Diff-Instruct: A Universal Approach for Transferring Knowledge From Pre-trained Diffusion Modelscited by 232
- 2021Gotta Go Fast When Generating Data with Score-Based Modelscited by 218
- 2021Diffusion Models for Implicit Image Segmentation Ensemblescited by 198
- 2022Fast Sampling of Diffusion Models via Operator Learningcited by 173
- 2023TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillationcited by 115
- 2023BOOT: Data-free Distillation of Denoising Diffusion Models with Bootstrappingcited by 96
- 2021CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Methodcited by 93
- 2023One-Step Diffusion Distillation via Deep Equilibrium Modelscited by 60
- 2023CDPMSR: Conditional Diffusion Probabilistic Models for Single Image Super-Resolutioncited by 21
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Citing papers per year: 2024: 1; 2025: 9; 2026: 3.
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- 2025Inductive Moment Matchingcited by 107
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 81
- 2024OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offscited by 22
- 2025Terminal Velocity Matchingcited by 17
- 2025Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instructioncited by 13
- 2025Flow Map Distillation Without Datacited by 13
- 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
- 2025Learning to Integrate Diffusion ODEs by Averaging the Derivativescited by 9
- 2025Understanding, Accelerating, and Improving MeanFlow Trainingcited by 3
- 2026PILD: Physics-Informed Learning via Diffusioncited by 2
- 2025Adaptive Discretization for Consistency Modelscited by 1
- 2026On the Memorization of Consistency Distillation for Diffusion Modelscited by 0
- 2026PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers17 Sep 2026
- 2026On the Memorization of Consistency Distillation for Diffusion Models26 Apr 2026
- 2026PILD: Physics-Informed Learning via Diffusion29 Jan 2026
- 2025Terminal Velocity Matching24 Nov 2025
- 2025Flow Map Distillation Without Data24 Nov 2025
- 2025Understanding, Accelerating, and Improving MeanFlow Training24 Nov 2025
- 2025Adaptive Discretization for Consistency Models20 Oct 2025
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillation17 Jun 2025
- 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation28 May 2025
- 2025Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction27 May 2025
- 2025Learning to Integrate Diffusion ODEs by Averaging the Derivatives20 May 2025
- 2025Inductive Moment Matching10 Mar 2025
- 2025Inductive Moment Matchingcited by 107
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 81
- 2025Terminal Velocity Matchingcited by 17
- 2025Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instructioncited by 13
- 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generationcited by 11
- 2025Learning to Integrate Diffusion ODEs by Averaging the Derivativescited by 9
- 2026PILD: Physics-Informed Learning via Diffusioncited by 2
- 2025Adaptive Discretization for Consistency Modelscited by 1
- 2026On the Memorization of Consistency Distillation for Diffusion Modelscited by 0
- 2026On the Memorization of Consistency Distillation for Diffusion Models26 Apr 2026
- 2026PILD: Physics-Informed Learning via Diffusion29 Jan 2026
- 2025Terminal Velocity Matching24 Nov 2025
- 2025Adaptive Discretization for Consistency Models20 Oct 2025
- 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillation17 Jun 2025
- 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation28 May 2025
- 2025Uni-Instruct: One-step Diffusion Model through Unified Diffusion Divergence Instruction27 May 2025
- 2025Learning to Integrate Diffusion ODEs by Averaging the Derivatives20 May 2025
- 2025Inductive Moment Matching10 Mar 2025
- 2024OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offscited by 22
- 2025Flow Map Distillation Without Datacited by 13
- 2025Understanding, Accelerating, and Improving MeanFlow Trainingcited by 3
- 2026PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solverscited by 0
- 2026PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers17 Sep 2026
- 2025Flow Map Distillation Without Data24 Nov 2025
- 2025Understanding, Accelerating, and Improving MeanFlow Training24 Nov 2025
- 2024OFTSR: One-Step Flow for Image Super-Resolution with Tunable Fidelity-Realism Trade-offs12 Dec 2024
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- 2025A Survey on Pre-Trained Diffusion Model Distillations
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- 2026PHDME: Physics-Informed Diffusion Models without Explicit Governing Equations
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