Boosting Diffusion Models with Moving Average Sampling in Frequency Domain

Diffusion models have recently brought a powerful revolution in image generation. Despite showing impressive generative capabilities, most of these models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. Instead of simply applying moving average to the denoised samples at different timesteps, we first map the denoised samples to data space and then perform moving average to avoid distribution shift across timesteps. In view that diffusion models evolve the recovery from low-frequency components to high-frequency details, we further decompose the samples into different frequency components and execute moving average separately on each component. We name the complete approach "Moving Average Sampling in Frequency domain (MASF)". MASF could be seamlessly integrated into mainstream pre-trained diffusion models and sampling schedules. Extensive experiments on both unconditional and conditional diffusion models demonstrate that our MASF leads to superior performances compared to the baselines, with almost negligible additional complexity cost.

Uncertainty-weighted Multi-tasking for $T_{1ρ}$ and T$_2$ Mapping in the Liver with Self-supervised Learning

Multi-parametric mapping of MRI relaxations in liver has the potential of revealing pathological information of the liver. A self-supervised learning based multi-parametric mapping method is proposed to map T$T_{1\rho}$ and T$_2$ simultaneously, by utilising the relaxation constraint in the learning process. Data noise of different mapping tasks is utilised to make the model uncertainty-aware, which adaptively weight different mapping tasks during learning. The method was examined on a dataset of 51 patients with non-alcoholic fatter liver disease. Results showed that the proposed method can produce comparable parametric maps to the traditional multi-contrast pixel wise fitting method, with a reduced number of images and less computation time. The uncertainty weighting also improves the model performance. It has the potential of accelerating MRI quantitative imaging.

Uncertainty-Aware Self-supervised Neural Network for Liver $T_{1ρ}$ Mapping with Relaxation Constraint

$T_{1\rho}$ mapping is a promising quantitative MRI technique for the non-invasive assessment of tissue properties. Learning-based approaches can map $T_{1\rho}$ from a reduced number of $T_{1\rho}$ weighted images, but requires significant amounts of high quality training data. Moreover, existing methods do not provide the confidence level of the $T_{1\rho}$ estimation. To address these problems, we proposed a self-supervised learning neural network that learns a $T_{1\rho}$ mapping using the relaxation constraint in the learning process. Epistemic uncertainty and aleatoric uncertainty are modelled for the $T_{1\rho}$ quantification network to provide a Bayesian confidence estimation of the $T_{1\rho}$ mapping. The uncertainty estimation can also regularize the model to prevent it from learning imperfect data. We conducted experiments on $T_{1\rho}$ data collected from 52 patients with non-alcoholic fatty liver disease. The results showed that our method outperformed the existing methods for $T_{1\rho}$ quantification of the liver using as few as two $T_{1\rho}$-weighted images. Our uncertainty estimation provided a feasible way of modelling the confidence of the self-supervised learning based $T_{1\rho}$ estimation, which is consistent with the reality in liver $T_{1\rho}$ imaging.