Given an unconditional diffusion model targeting a joint model $\pi(x, y)$, using it to perform conditional simulation $\pi(x \mid y)$ is still largely an open question and is typically achieved by learning conditional drifts to the denoising SDE after the fact. In this work, we express \emph{exact} conditional simulation within the \emph{approximate} diffusion model as an inference problem on an augmented space corresponding to a partial SDE bridge. This perspective allows us to implement efficient and principled particle Gibbs and pseudo-marginal samplers marginally targeting the conditional distribution $\pi(x \mid y)$. Contrary to existing methodology, our methods do not introduce any additional approximation to the unconditional diffusion model aside from the Monte Carlo error. We showcase the benefits and drawbacks of our approach on a series of synthetic and real data examples.

A recent line of research has exploited pre-trained generative diffusion models as priors for solving Bayesian inverse problems. We contribute to this research direction by designing a sequential Monte Carlo method for linear-Gaussian inverse problems which builds on ``decoupled diffusion", where the generative process is designed such that larger updates to the sample are possible. The method is asymptotically exact and we demonstrate the effectiveness of our Decoupled Diffusion Sequential Monte Carlo (DDSMC) algorithm on both synthetic as well as protein and image data. Further, we demonstrate how the approach can be extended to discrete data.

Diffusion models have recently achieved outstanding results in the field of image super-resolution. These methods typically inject low-resolution (LR) images via ControlNet. In this paper, we first explore the temporal dynamics of information infusion through ControlNet, revealing that the input from LR images predominantly influences the initial stages of the denoising process. Leveraging this insight, we introduce a novel timestep-aware diffusion model that adaptively integrates features from both ControlNet and the pre-trained Stable Diffusion (SD). Our method enhances the transmission of LR information in the early stages of diffusion to guarantee image fidelity and stimulates the generation ability of the SD model itself more in the later stages to enhance the detail of generated images. To train this method, we propose a timestep-aware training strategy that adopts distinct losses at varying timesteps and acts on disparate modules. Experiments on benchmark datasets demonstrate the effectiveness of our method.

Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent variable space and thus challenging to approximate with parametric models. To address this problem, we propose an efficient sampling-based training strategy, wherein the training of a pBNN is formulated as simulating a Feynman-Kac model. We then describe variations of sequential Monte Carlo samplers that allow us to simultaneously estimate the parameters and the latent posterior distribution of this model at a tractable computational cost. Using various synthetic and real-world datasets we show that our proposed training scheme outperforms the state of the art in terms of predictive performance.

Vision-language models such as CLIP have shown great impact on diverse downstream tasks for zero-shot or label-free predictions. However, when it comes to low-level vision such as image restoration their performance deteriorates dramatically due to corrupted inputs. In this paper, we present a degradation-aware vision-language model (DA-CLIP) to better transfer pretrained vision-language models to low-level vision tasks as a multi-task framework for image restoration. More specifically, DA-CLIP trains an additional controller that adapts the fixed CLIP image encoder to predict high-quality feature embeddings. By integrating the embedding into an image restoration network via cross-attention, we are able to pilot the model to learn a high-fidelity image reconstruction. The controller itself will also output a degradation feature that matches the real corruptions of the input, yielding a natural classifier for different degradation types. In addition, we construct a mixed degradation dataset with synthetic captions for DA-CLIP training. Our approach advances state-of-the-art performance on both degradation-specific and unified image restoration tasks, showing a promising direction of prompting image restoration with large-scale pretrained vision-language models. Our code is available at https://github.com/Algolzw/daclip-uir.

This paper presents a stochastic differential equation (SDE) approach for general-purpose image restoration. The key construction consists in a mean-reverting SDE that transforms a high-quality image into a degraded counterpart as a mean state with fixed Gaussian noise. Then, by simulating the corresponding reverse-time SDE, we are able to restore the origin of the low-quality image without relying on any task-specific prior knowledge. Crucially, the proposed mean-reverting SDE has a closed-form solution, allowing us to compute the ground truth time-dependent score and learn it with a neural network. Moreover, we propose a maximum likelihood objective to learn an optimal reverse trajectory that stabilizes the training and improves the restoration results. The experiments show that our proposed method achieves highly competitive performance in quantitative comparisons on image deraining, deblurring, and denoising, setting a new state-of-the-art on two deraining datasets. Finally, the general applicability of our approach is further demonstrated via qualitative results on image super-resolution, inpainting, and dehazing. Code is available at https://github.com/Algolzw/image-restoration-sde.

This letter is concerned with solving continuous-discrete Gaussian smoothing problems by using the Taylor moment expansion (TME) scheme. In the proposed smoothing method, we apply the TME method to approximate the transition density of the stochastic differential equation in the dynamic model. Furthermore, we derive a theoretical error bound (in the mean square sense) of the TME smoothing estimates showing that the smoother is stable under weak assumptions. Numerical experiments are presented in order to illustrate practical use of the method.

Autonomous ships are expected to improve the level of safety and efficiency in future maritime navigation. Such vessels need perception for two purposes: to perform autonomous situational awareness and to monitor the integrity of the sensor system itself. In order to meet these needs, the perception system must fuse data from novel and traditional perception sensors using Artificial Intelligence (AI) techniques. This article overviews the recognized operational requirements that are imposed on regular and autonomous seafaring vessels, and then proceeds to consider suitable sensors and relevant AI techniques for an operational sensor system. The integration of four sensors families is considered: sensors for precise absolute positioning (Global Navigation Satellite System (GNSS) receivers and Inertial Measurement Unit (IMU)), visual sensors (monocular and stereo cameras), audio sensors (microphones), and sensors for remote-sensing (RADAR and LiDAR). Additionally, sources of auxiliary data, such as Automatic Identification System (AIS) and external data archives are discussed. The perception tasks are related to well-defined problems, such as situational abnormality detection, vessel classification, and localization, that are solvable using AI techniques. Machine learning methods, such as deep learning and Gaussian processes, are identified to be especially relevant for these problems. The different sensors and AI techniques are characterized keeping in view the operational requirements, and some example state-of-the-art options are compared based on accuracy, complexity, required resources, compatibility and adaptability to maritime environment, and especially towards practical realization of autonomous systems.

This paper is concerned with the estimation of unknown drift functions of stochastic differential equations (SDEs) from observations of their sample paths. We propose to formulate this as a non-parametric Gaussian process regression problem and use an Ito-Taylor expansion for approximating the SDE. To address the computational complexity problem of Gaussian process regression, we cast the model in an equivalent state-space representation, such that (non-linear) Kalman filters and smoothers can be used. The benefit of these methods is that computational complexity scales linearly with respect to the number of measurements and hence the method remains tractable also with large amounts of data. The overall complexity of the proposed method is O(N log N), where N is the number of measurements, due to the requirement of sorting the input data. We evaluate the performance of the proposed method using simulated data as well as with real-data applications to sunspot activity and electromyography.