Related papers: Dynamical Regimes of Diffusion Models
We train a generative diffusion model (DM) to simulate ultra-relativistic heavy-ion collisions from end to end. The model takes initial entropy density profiles as input and produces two-dimensional final particle spectra, successfully…
Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal…
Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion…
Geophysical inverse problems are often ill-posed and admit multiple solutions. Conventional discriminative methods typically yield a single deterministic solution, which fails to model the posterior distribution, cannot generate diverse…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…
Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
Diffusion models have demonstrated impressive capabilities in synthesizing diverse content. However, despite their high-quality outputs, these models often perpetuate social biases, including those related to gender and race. These biases…
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Diffusion models are capable of impressive feats of image generation with uncommon juxtapositions such as astronauts riding horses on the moon with properly placed shadows. These outputs indicate the ability to perform compositional…
We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
Practically, training diffusion models typically requires explicit time conditioning to guide the network through the denoising sampling process. Especially in deterministic methods like DDIM, the absence of time conditioning leads to…
Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static…
Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is…