# A framework for conditional diffusion modelling with applications in motif scaffolding for protein design

arXiv: https://arxiv.org/abs/2312.09236 · HTML: https://mlsanity.com/paper/2312.09236/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 29 of its 39 references that are in the map.
- First posted on arXiv 14 Dec 2023.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (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)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [Bayesian Learning via Neural Schr"odinger-F"ollmer Flows](https://mlsanity.com/paper/2111.10510/) (2021)
- [Generating Novel, Designable, and Diverse Protein Structures by Equivariantly Diffusing Oriented Residue Clouds](https://mlsanity.com/paper/2301.12485/) (2023)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems](https://mlsanity.com/paper/2306.07526/) (2023)
- [First Hitting Diffusion Models for Generating Manifold, Graph and Categorical Data](https://mlsanity.com/paper/2209.01170/) (2022)
- [Geometric Neural Diffusion Processes](https://mlsanity.com/paper/2307.05431/) (2023)

## Built on by (most cited first, 22 of 22)

- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024)
- [Sequential Controlled Langevin Diffusions](https://mlsanity.com/paper/2412.07081/) (2024)
- [DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transform](https://mlsanity.com/paper/2406.01781/) (2024)
- [Improved motif-scaffolding with SE(3) flow matching](https://mlsanity.com/paper/2401.04082/) (2024)
- [Out of Many, One: Designing and Scaffolding Proteins at the Scale of the Structural Universe with Genie 2](https://mlsanity.com/paper/2405.15489/) (2024)
- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [RNA-FrameFlow: Flow Matching for de novo 3D RNA Backbone Design](https://mlsanity.com/paper/2406.13839/) (2024)
- [TFG-Flow: Training-free Guidance in Multimodal Generative Flow](https://mlsanity.com/paper/2501.14216/) (2025)
- [Constrained Diffusion for Protein Design with Hard Structural Constraints](https://mlsanity.com/paper/2510.14989/) (2025)
- [On diffusion posterior sampling via sequential Monte Carlo for zero-shot scaffolding of protein motifs](https://mlsanity.com/paper/2412.05788/) (2024)
- [Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions](https://mlsanity.com/paper/2501.19373/) (2025)
- [MotifBench: A standardized protein design benchmark for motif-scaffolding problems](https://mlsanity.com/paper/2502.12479/) (2025)
- [Test-Time Conditioning with Representation-Aligned Visual Features](https://mlsanity.com/paper/2602.03753/) (2026)
- [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026)
- [Physics-aligned Schr"odinger bridge](https://mlsanity.com/paper/2409.17825/) (2024)
- [EnzyControl: Adding Functional and Substrate-Specific Control for Enzyme Backbone Generation](https://mlsanity.com/paper/2510.25132/) (2025)
- [A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2606.12710/) (2026)
- [Dynamic Diffusion Schr"odinger Bridge in Astrophysical Observational Inversions](https://mlsanity.com/paper/2506.08065/) (2025)
- [Infinite-dimensional generative diffusions via Doob's h-transform](https://mlsanity.com/paper/2602.06621/) (2026)
- [Conditional Diffusion Under Linear Constraints: Langevin Mixing and Information-Theoretic Guarantees](https://mlsanity.com/paper/2605.05387/) (2026)
- [Commitment Before Realization: When Classifier-Free Guidance Becomes Unnecessary in Masked Diffusion Language Models](https://mlsanity.com/paper/2608.08082/) (2026)

## Abstract (arXiv)

Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address this motif scaffolding problem and have shown early experimental success in some cases. In the diffusion paradigm, motif scaffolding is treated as a conditional generation task, and several conditional generation protocols were proposed or imported from the Computer Vision literature. However, most of these protocols are motivated heuristically, e.g. via analogies to Langevin dynamics, and lack a unifying framework, obscuring connections between the different approaches. In this work, we unify conditional training and conditional sampling procedures under one common framework based on the mathematically well-understood Doob's h-transform. This new perspective allows us to draw connections between existing methods and propose a new variation on existing conditional training protocols. We illustrate the effectiveness of this new protocol in both, image outpainting and motif scaffolding and find that it outperforms standard methods.