Related papers: Noise Schedule Design for Diffusion Models: An Opt…
We consider optimal control of fractional in time (subdiffusive, i.e., for $% 0<\gamma <1$) semilinear parabolic PDEs associated with various notions of diffusion operators in an unifying fashion. Under general assumptions on the…
Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an…
Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…
We analyze structure-preserving model order reduction methods for Ornstein-Uhlenbeck processes and linear S(P)DEs with multiplicative noise based on balanced truncation. For the first time, we include in this study the analysis of non-zero…
Diffusion models generate data by learning to reverse a forward process, where samples are progressively perturbed with Gaussian noise according to a predefined noise schedule. From a geometric perspective, each noise schedule corresponds…
We study stochastic optimal control problems for (possibly degenerate) McKean-Vlasov controlled diffusions and obtain discrete-time as well as finite interacting particle approximations. (i) Under mild assumptions, we first prove the…
Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of…
Optimal input design is an important step of the identification process in order to reduce the model variance. In this work a D-optimal input design method for finite-impulse-response-type nonlinear systems is presented. The optimization of…
This paper is concerned with the partial information optimal control problem of wa controlled forward-backward stochastic differential equation of jump diffusion with correlated noises between the system and the observation. For this type…
In this work, we study the problem of choosing the discretisation schedule for sampling from masked discrete diffusion models in terms of the information geometry of the induced probability path. Specifically, we show that the optimal…
Super- and sub- diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub- diffusions driven by fractional…
Addressing real-world optimization problems becomes particularly challenging when analytic objective functions or constraints are unavailable. While numerous studies have addressed the issue of unknown objectives, limited research has…
Despite many attempts to leverage pre-trained text-to-image models (T2I) like Stable Diffusion (SD) for controllable image editing, producing good predictable results remains a challenge. Previous approaches have focused on either…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method,…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
We consider the problem of estimating the direction of arrival of a signal embedded in $K$-distributed noise, when secondary data which contains noise only are assumed to be available. Based upon a recent formula of the Fisher information…
A new class of cost functionals for optimal control of quantum systems which produces controls which are sparse in frequency and smooth in time is proposed. This is achieved by penalizing a suitable time-frequency representation of the…
Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can…
Classifier-guided diffusion models have emerged as a powerful approach for conditional image generation, but they suffer from overconfident predictions during early denoising steps, causing the guidance gradient to vanish. This paper…