mlsanityData to 14 Oct 2026

Score-based Generative Modeling Through Backward Stochastic Differential Equations: Inversion and Generation

arXiv 2304.13224 ↗First posted 26 Apr 2023cs.LG cs.AIcited by 5

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our model can determine the initial conditions necessary to reach a desired terminal distribution by adapting an existing score function. We demonstrate the theoretical guarantees of the model, the benefits of using Lipschitz networks for score matching, and its potential applications in various areas such as diffusion inversion, conditional diffusion, and uncertainty quantification. Our work represents a contribution to the field of score-based generative learning and offers a promising direction for solving real-world problems.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 22 of its 59 references that are in the map. First posted on arXiv 26 Apr 2023.

Builds on

22 of 59 references.

Closest ancestors · 7

Same direction, newest first

  1. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  2. 2022Riemannian Score-Based Generative Modelling6 Feb
  3. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matching5 Jun
  4. 2021Gotta Go Fast When Generating Data with Score-Based Models28 May
  5. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  6. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  7. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 15

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  2. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,355
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  4. 2021SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equationscited by 1,937
  5. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,778
  6. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
  7. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  8. 2022Diffusion Probabilistic Modeling for Video Generationcited by 238
  9. 2022Diffusion-based Time Series Imputation and Forecasting with Structured State Space Modelscited by 198
  10. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 191
  11. 2023Leapfrog Diffusion Model for Stochastic Trajectory Predictioncited by 132
  12. 2018Convergence of the Deep BSDE Method for Coupled FBSDEscited by 43
3 more
  1. 2023Zero-shot-Learning Cross-Modality Data Translation Through Mutual Information Guided Stochastic Diffusioncited by 6
  2. 2019Introduction to Solving Quant Finance Problems with Time-Stepped FBSDE and Deep Learningcited by 2
  3. 2021Value Function Estimators for Feynman-Kac Forward-Backward SDEs in Stochastic Optimal Controlcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 0; 2025: 3; 2026: 1.

5 papers.

  1. 2025Free-Form Motion Control: Controlling the 6D Poses of Camera and Objects in Video Generationcited by 15
  2. 2025A Diffusion-Based Framework for Terrain-Aware Remote Sensing Image Reconstructioncited by 6
  3. 2023Diffusion Models for Generative Artificial Intelligence: An Introduction for Applied Mathematicianscited by 5
  4. 2025Vision-Driven Prompt Optimization for Large Language Models in Multimodal Generative Taskscited by 0
  5. 2026GaiaFlow: Semantic-Guided Diffusion Tuning for Carbon-Frugal Searchcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2022A Flexible Diffusion Model
  2. 2025A Malliavin calculus approach to score functions in diffusion generative models
  3. 2024Score-based Diffusion Models via Stochastic Differential Equations -- a Technical Tutorial
  4. 2026A Stochastic Analysis Perspective on Diffusion Models
  5. 2023Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation
  6. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  7. 2024Discrete vs. Continuous Trade-offs for Generative Models
  8. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models