Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data

מושגי ליבה

Diffusion models trained on corrupted data can outperform clean data models for image restoration tasks.

תקציר

The article introduces Ambient Diffusion Posterior Sampling (A-DPS) as a framework for solving inverse problems using diffusion models trained on linearly corrupted data. The method leverages generative models pre-trained on one type of corruption to perform posterior sampling conditioned on measurements from a different forward process. Experiments conducted on natural image datasets and multi-coil MRI show that A-DPS can outperform models trained on clean data in both speed and performance for various tasks. The study extends the Ambient Diffusion framework to train MRI models with Fourier subsampled multi-coil MRI measurements at different acceleration factors. Results indicate that models trained on highly subsampled data are better priors for solving inverse problems in the high acceleration regime than those trained on fully sampled data. Overall, the article highlights the potential of generative models trained on corrupted data for image restoration tasks.

סטטיסטיקה

We open-source our code and the trained Ambient Diffusion MRI models: github.com/utcsilab/ambient-diffusion-mri.
For some applications, it is expensive or impossible to acquire fully observed or uncorrupted data.
Prior works have shown how to train Generative Adversarial Networks (GANs), flow models, and restoration models with corrupted training data.
Our experiments show that A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance.
We further extend the Ambient Diffusion framework to train MRI models with access only to Fourier subsampled multi-coil MRI measurements at various acceleration factors (R= 2, 4, 6, 8).

ציטוטים

"Our method leverages a generative model pre-trained on one type of corruption to perform posterior sampling conditioned on measurements from a potentially different forward process."
"A-DPS can sometimes outperform models trained on clean data for several image restoration tasks in both speed and performance."
"We open-source our code and the trained Ambient Diffusion MRI models."

תובנות מפתח מזוקקות מ:

Ambient Diffusion Posterior Sampling

by Asad Aali,Gi... ב- arxiv.org 03-14-2024

https://arxiv.org/pdf/2403.08728.pdf

שאלות מעמיקות

How does the use of diffusion models trained on corrupted data impact generalization to unseen datasets

Training diffusion models on corrupted data can have both positive and negative impacts on generalization to unseen datasets. On the one hand, using corrupted data for training can help the model learn robust features that are more resilient to noise and corruption in real-world scenarios. This can improve the model's ability to generalize to unseen datasets with similar levels of corruption. Additionally, training on corrupted data can prevent overfitting and encourage the model to focus on learning essential features rather than memorizing specific examples.
On the other hand, there is a risk that diffusion models trained on corrupted data may not generalize well to clean or differently corrupted datasets. The learned priors from the training data might be biased towards specific types of corruption present in the training set, leading to suboptimal performance when applied to different types of corruptions or noise levels. Therefore, careful evaluation and validation on diverse datasets are crucial to assess how well diffusion models trained on corrupted data generalize across different scenarios.

What are the implications of relying solely on Fourier subsampled multi-coil MRI measurements for training

Relying solely on Fourier subsampled multi-coil MRI measurements for training has several implications for MRI reconstruction tasks:

Limited Training Data: Using only subsampled measurements restricts access to fully sampled ground truth images during training. This limitation may affect the model's ability to learn high-quality image reconstructions as it lacks direct supervision from complete images.

Generalization Challenges: Models trained solely on subsampled MRI measurements may struggle with generalizing their reconstructions beyond the acceleration factors seen during training. They might perform well within those specific ranges but could face difficulties when applied outside those bounds.

Performance Trade-offs: While relying exclusively on subsampled measurements reduces computational complexity and resource requirements during training, it may come at a cost of sacrificing reconstruction quality compared to methods that incorporate additional information or constraints.

Need for Robust Priors: Given limited information from subsampled measurements, ensuring robust prior knowledge through techniques like Ambient Diffusion Posterior Sampling (A-DPS) becomes crucial for accurate MRI reconstruction at higher acceleration factors where full sampling is not available.

How might incorporating additional types of corruption during training affect the performance of A-DPS

Incorporating additional types of corruption during training in A-DPS can have varying effects depending on how these corruptions align with real-world scenarios:

Enhanced Robustness: Introducing diverse forms of corruption during training can enhance the model's ability to handle various sources of noise and artifacts commonly encountered in practice.

Improved Generalization: By exposing the model to a range of corruptions, it learns more generalized representations that can adapt better when faced with unseen challenges during inference.

3 .Complexity vs Performance Trade-off: However, adding too many types of corruptions could increase model complexity without necessarily improving performance significantly if these corruptions do not align closely with test-time conditions.
4 .Hyperparameter Sensitivity: The choice and balance between different types of corrupting mechanisms need careful consideration as they impact hyperparameters tuning strategies such as likelihood weighting γt selection in A-DPS algorithm.