On the Theory of Stochastic Processes, with Particular Reference to Applications

By W. Feller. 1949

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

Deep Unsupervised Learning using Nonequilibrium Thermodynamics (2015, background): “on model. For both Gaussian and binomial diffusion, for continuous diffusion (limit of small step size ) the reversal of the diffusion process has the identical functional form as the forward process [8]. Since q x(t)jx(t 1) is a Gaussian (binomial) distribution, and if ( tis small, then q x t 1)jx(”
Structured Denoising Diffusion Models in Discrete State-Spaces (2021, background): “When the number of time steps T goes to infinity, both the forward process and the reverse process share the same functional form [36, 12], in the sense that the true posterior q(xt 1|xt) becomes fully conditionally independent.”
Unsupervised Medical Image Translation With Adversarial Diffusion Models (2022, background): “Under large T and small β t , the reverse transition probability between x t − 1 and x t can be approximated as a Gaussian distribution [56], [57]: Diffusion models typically operationalize each reverse diffusion step as mapping through a neural network that provides estimates for µ and/or (cid:54)…”
Blended Diffusion for Text-driven Editing of Natural Images (2021, background): “That is, starting from a Gaussian noise sample, xT ∼ N (0, I), a reverse sequence is generated by sampling the posteriors q(xt−1|xt), which were shown to also be Gaussian distributions [16, 45].”
Diffusion Models in Vision: A Survey (2022, background): “Moreover, if each (βt)t=1 1, then the reverse steps p(xt−1|xt) have the same functional form as the forward process p(xt|xt−1) [1], [66].”
DreamLLM: Synergistic Multimodal Comprehension and Creation (2023, background): “…noise z T ∼ N ( 0 , I ) as a Markov Chain with transition approximated by a Gaussian model p ξ ( z t − 1 | z t ) := N ( µ ξ ( z t ) , σ 2 t I ) , which relates to an optimal MSE denoiser since q ( z t − 1 | z t , z 1 ) is Gaussian with enough timestamps (Feller, 1949; Sohl-Dickstein et al., 2015).”
Building Normalizing Flows with Stochastic Interpolants (2022, unknown): “Namely, the SDE must evolve for infinite time to connect the distributions, the parameterization of the time steps remains heuristic (Feller, 1949; Xiao et al., 2022), and the criticality of noise, as well as the score, is not absolutely apparent (Bansal et al.”
Tackling the Generative Learning Trilemma with Denoising Diffusion GANs (2021, background): “First, in the limit of infinitesimal step size βt, the product in the Bayes’ rule is dominated by q(xt|xt−1) and the reversal of the diffusion process takes an identical functional form as the forward process (Feller, 1949).”