We propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process to solve posterior sampling with diffusion prior. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels.

Our approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems. For example, we achieve a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, which is an improvement of 9.12dB compared to existing methods.

We provide a notebook for detailed guidance .

• python 3.8
• PyTorch 2.3
• CUDA 12.1

Lower version of PyTorch with proper CUDA should work but not be fully tested.

# in DAPS folder

conda create -n DAPS python=3.8
conda activate DAPS

pip install -r requirements.txt

# (optional) install PyTorch with proper CUDA
conda install pytorch==2.3.0 torchvision==0.18.0 torchaudio==2.3.0 pytorch-cuda=12.1 -c pytorch -c nvidia

We use bkse for nonlinear blurring and motionblur for motion blur. No further action required then.

Download the public available FFHQ checkpoint (ffhq_10m.pt) here.

# in DAPS folder

mkdir checkpoint
mv {DOWNLOAD_DIR}/ffqh_10m.pt checkpoint/ffhq256.pt

(Optional) For nonlinear deblur task, we need the pretrained model from bkse at here:

# in DAPS folder

mv {DOWNLOAD_DIR}/GOPRO_wVAE.pth forward_operator/bkse/experiments/pretrained

You can add any FFHQ256 images you like to dataset/demo folder

Make a folder to save results:

mkdir results

Now you are ready for run. For phase retrieval with DAPS-1k in 4 runs for $10$ demo images in dataset/demo:

python posterior_sample.py \
+data=demo \
+model=ffhq256ddpm \
+task=phase_retrieval \
+sampler=edm_daps \
save_dir=results \
num_runs=4 \
sampler.diffusion_scheduler_config.num_steps=5 \
sampler.annealing_scheduler_config.num_steps=200 \
batch_size=10 \
data.start_id=0 data.end_id=10 \
name=phase_retrieval_demo \
gpu=0

It takes about $8$ minutes ($2$ for each run) and $6G$ GPU memory on a single NVIDIA A100-SXM4-80GB GPU. The results are saved at foloder \results.

python posterior_sample.py \
+data=demo \
+model=ffhq256ddpm \
+task={TASK_NAME} \
+sampler=edm_daps \
save_dir=results \
num_runs=1 \
sampler.diffusion_scheduler_config.num_steps=5 \
sampler.annealing_scheduler_config.num_steps=200 \
batch_size=10 \
data.start_id=0 data.end_id=10 \
name={SUB_FOLDER_NAME} \
gpu=0

replace the {TASK_NAME} by one of following:

• phase_retrieval: phase retrival of oversample ratio of $2.0$

• down_sampling: super resolution ($\times 4$)

• inpainting: 128x128 box inpainting

• inpainting_rand: $70%$ random inpainting

• gaussian_blur: gaussian deblur of kernel size $61$ and intensity $3$

• motion_blur: gaussian deblur of kernel size $61$ and intensity $0.5$

• nonlinear_blur: nonlinear deblur of default setting in bkse repo

• hdr: high dynamic range reconstruction of factor $2$

If you find our work interesting, please consider citing

@misc{zhang2024improvingdiffusioninverseproblem,
      title={Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing}, 
      author={Bingliang Zhang and Wenda Chu and Julius Berner and Chenlin Meng and Anima Anandkumar and Yang Song},
      year={2024},
      eprint={2407.01521},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2407.01521}, 
}