Related papers: Score Reversal Is Not Free for Quantum Diffusion M…

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…

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…

Generative neural image compression supports data representation at extremely low bitrate, synthesizing details at the client and consistently producing highly realistic images. By leveraging the similarities between quantization error and…

We investigate the problem of optimally reversing the action of an arbitrary quantum channel C which acts independently on each component of an ensemble of n identically prepared d-dimensional quantum systems. In the limit of large…

Based on a proposed classical explanation, the quantum mechanical "decay of the wave packet" is shown to simply result from sub-quantum diffusion with a specific diffusivity varying in time due to a particle's changing thermal environment.…

In this note we solve a general statistical inverse problem under absence of knowledge of both the noise level and the noise distribution via application of the (modified) heuristic discrepancy principle. Hereby the unbounded (non-Gaussian)…

Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…

We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be…

The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One ("Loschmidt echo") is related to "time reversal", while the other is related to "driving…

Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…

We introduce a technique for recovering noise-free observables in noisy quantum systems by combining the results of many slightly different experiments. Our approach is applicable to a variety of quantum systems but we illustrate it with…

Most existing graph diffusion models have significant bias problems. We observe that the forward diffusion's maximum perturbation distribution in most models deviates from the standard Gaussian distribution, while reverse sampling…

Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…

Computational level explanations based on optimal feedback control with signal-dependent noise have been able to account for a vast array of phenomena in human sensorimotor behavior. However, commonly a cost function needs to be assumed for…

This book presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward…

Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we…

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system,…

Momentum diffusion is a possible mechanism for driving macroscopic quantum systems towards classical behaviour. Experimental tests of this hypothesis rely on a precise estimation of the strength of this diffusion. We show that…

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models,…

The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…