mlsanityData to 14 Oct 2026

Diffusion Models With Learned Adaptive Noise

arXiv 2312.13236 ↗First posted 20 Dec 2023cs.LG cs.CVcited by 51

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect performance. In this paper, we explore whether the diffusion process can be learned from data. Our work is grounded in Bayesian inference and seeks to improve log-likelihood estimation by casting the learned diffusion process as an approximate variational posterior that yields a tighter lower bound (ELBO) on the likelihood. A widely held assumption is that the ELBO is invariant to the noise process: our work dispels this assumption and proposes multivariate learned adaptive noise (MULAN), a learned diffusion process that applies noise at different rates across an image. Specifically, our method relies on a multivariate noise schedule that is a function of the data to ensure that the ELBO is no longer invariant to the choice of the noise schedule as in previous works. Empirically, MULAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet and reduces the number of training steps by 50%. We provide the code, along with a blog post and video tutorial on the project page: https://s-sahoo.com/MuLAN

Key facts. Cited by 51 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 51 of its 70 references that are in the map. First posted on arXiv 20 Dec 2023.

Builds on

51 of 70 references.

Closest ancestors · 23

Same direction, newest first

  1. 2023DiffEnc: Variational Diffusion with a Learned Encoder30 Oct
  2. 2023Neural Diffusion Models12 Oct
  3. 2023SVNR: Spatially-variant Noise Removal with Denoising Diffusion28 Jun
  4. 2023InfoDiffusion: Representation Learning Using Information Maximizing Diffusion Models14 Jun
  5. 2023Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs6 May
  6. 2023Reflected Diffusion Models10 Apr
  7. 2023Diffusion Schr"odinger Bridge Matching29 Mar
  8. 2023Minimizing Trajectory Curvature of ODE-based Generative Models27 Jan
  9. 2023Simple diffusion: End-to-end diffusion for high resolution images26 Jan
  10. 2023On the Importance of Noise Scheduling for Diffusion Models26 Jan
  11. 2022Blurring Diffusion Models12 Sep
  12. 2022A Flexible Diffusion Model17 Jun
11 more
  1. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching16 Jun
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  3. 2021Diffusion Autoencoders: Toward a Meaningful and Decodable Representation30 Nov
  4. 2021Diffusion Normalizing Flow14 Oct
  5. 2021Variational Diffusion Models1 Jul
  6. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  7. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  8. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  9. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 28

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  5. 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
  6. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  7. 2016Conditional Image Generation with PixelCNN Decoderscited by 862
  8. 2016Pixel Recurrent Neural Networkscited by 816
  9. 2018Image Transformercited by 772
  10. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  11. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 447
  12. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 417
16 more
  1. 2017PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examplescited by 244
  2. 2022Lossy Image Compression with Conditional Diffusion Modelscited by 170
  3. 2022Generative Modelling With Inverse Heat Dissipationcited by 167
  4. 2022Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modelingcited by 127
  5. 2021Deep Generative Learning via Schr"odinger Bridgecited by 104
  6. 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 98
  7. 2017Good Semi-supervised Learning that Requires a Bad GANcited by 86
  8. 2021PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Priorcited by 80
  9. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  10. 2019Reparameterizable Subset Sampling via Continuous Relaxationscited by 70
  11. 2013RNADE: The real-valued neural autoregressive density-estimatorcited by 66
  12. 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
  13. 2021Autoregressive Quantile Flows for Predictive Uncertainty Estimationcited by 15
  14. 2022Deep Multi-Modal Structural Equations For Causal Effect Estimation With Unstructured Proxiescited by 13
  15. 2022Semi-Autoregressive Energy Flows: Exploring Likelihood-Free Training of Normalizing Flowscited by 9
  16. 2022Semi-Parametric Inducing Point Networks and Neural Processescited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 6; 2025: 22; 2026: 23.

51 papers.

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  1. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  2. 2025Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Modelscited by 409
  3. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 155
  4. 2025The Diffusion Dualitycited by 135
  5. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
  6. 2025Noise Hypernetworks: Amortizing Test-Time Compute in Diffusion Modelscited by 35
  7. 2025Esoteric Language Models: A Family of Any-Order Diffusion LLMscited by 34
  8. 2026Scaling Beyond Masked Diffusion Language Modelscited by 27
  9. 2025SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationscited by 23
  10. 2026Learn from Your Mistakes: Self-Correcting Masked Diffusion Modelscited by 13
  11. 2025Shaping Inductive Bias in Diffusion Models through Frequency-Based Noise Controlcited by 11
  12. 2024Discrete Diffusion Language Model for Efficient Text Summarizationcited by 8
38 more
  1. 2025Learning Flexible Forward Trajectories for Masked Molecular Diffusioncited by 7
  2. 2025Adaptive Destruction Processes for Diffusion Samplerscited by 6
  3. 2026Unifying Masked Diffusion Models with Various Generation Orders and Beyondcited by 6
  4. 2025Guided Star-Shaped Masked Diffusioncited by 5
  5. 2026Spectrally-Guided Diffusion Noise Schedulescited by 5
  6. 2024Enhancing Sample Generation of Diffusion Models using Noise Level Correctioncited by 4
  7. 2025A Comprehensive Review on Noise Control of Diffusion Modelcited by 4
  8. 2025A First-order Generative Bilevel Optimization Framework for Diffusion Modelscited by 4
  9. 2026Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Featurescited by 4
  10. 2025WAVE: Warp-Based View Guidance for Consistent Novel View Synthesis Using a Single Imagecited by 3
  11. 2025Masked Diffusion Models are Secretly Learned-Order Autoregressive Modelscited by 3
  12. 2026A Minimum Variance Path Principle for Accurate and Stable Score-Based Density Ratio Estimationcited by 3
  13. 2024ComboStoc: Combinatorial Stochasticity for Diffusion Generative Modelscited by 2
  14. 2025Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noisecited by 2
  15. 2026StableHand: Quality-Aware Flow Matching for World-Space Dual-Hand Motion Estimation from Egocentric Videocited by 2
  16. 2026Set Diffusion: Interpolating Token Orderings Between Autoregression and Diffusion for Fast and Flexible Decodingcited by 2
  17. 2026Unlocking Lossless Speedups in LLMs via Discrete Diffusioncited by 2
  18. 2025Squeezed Diffusion Modelscited by 1
  19. 2025[Re] Improving Interpretation Faithfulness for Vision Transformerscited by 1
  20. 2025Diffusion^2: Dual Diffusion Model with Uncertainty-Aware Adaptive Noise for Momentary Trajectory Predictioncited by 1
  21. 2026Towards Latent Diffusion Suitable For Textcited by 1
  22. 2026Insertion Based Sequence Generation with Learnable Order Dynamicscited by 1
  23. 2026Variational Trajectory Optimization of Anisotropic Diffusion Schedulescited by 1
  24. 2026WaveFilter: Enhancing the Long-Context Capability of Diffusion LLMs via Wavelet-Guided KV Cache Filteringcited by 1
  25. 2026Spatially Adaptive Noise Injectioncited by 1
  26. 2025Is Noise Conditioning Necessary? A Unified Theory of Unconditional Graph Diffusion Modelscited by 0
  27. 2025DACA-Net: A Degradation-Aware Conditional Diffusion Network for Underwater Image Enhancementcited by 0
  28. 2025Adapting Noise to Data: Generative Flows from 1D Processescited by 0
  29. 2025Variational Polya Treecited by 0
  30. 2025Breaking the Likelihood-Quality Trade-off in Diffusion Models by Merging Pretrained Expertscited by 0
  31. 2026A Gaussian Perspective for Distributional Discrepancy in Generative Diffusion Modelscited by 0
  32. 2026Can We Change the Stroke Size for Easier Diffusion?cited by 0
  33. 2026Region-Adaptive Generative Compression with Spatially Varying Diffusion Modelscited by 0
  34. 2026Learning Normalized Energy Models for Linear Inverse Problemscited by 0
  35. 2026Reinforcement Learning: From Algorithms To Foundation Modelscited by 0
  36. 2026Retrieval-Augmented Diffusion Modeling for Stochastic Discount Factor Portfolioscited by 0
  37. 2026ExploreNet: Learning Where to Explore in Diffusion GRPOcited by 0
  38. 2026Clock Diffusion: Efficient Semi-Autoregressive Continuous Diffusion Language Modelscited by 0

50 most cited of 51 All 51 (JSON)

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  1. 2023Where to Diffuse, How to Diffuse, and How to Get Back: Automated Learning for Multivariate Diffusions
  2. 2025Diffusion Models: A Mathematical Introduction
  3. 2025Information Theoretic Learning for Diffusion Models with Warm Start
  4. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation
  5. 2024Non-Normal Diffusion Models
  6. 2024Learning Diffusion Model from Noisy Measurement using Principled Expectation-Maximization Method
  7. 2025A Mixture-Based Framework for Guiding Diffusion Models
  8. 2024Blue noise for diffusion models