Reverse-time diffusion equation models

By B.D.O. Anderson. 1982

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In Generative Models

Citations in the corpus

Score-based Generative Modeling in Latent Space (2021, background): “…used in this paper can be written in the general form The reverse of this diffusion process is also a diffusion process running backwards in time [105, 2], deﬁned by where d ¯ w denotes a standard Wiener process going backwards in time, dt now represents a negative inﬁnitesimal time increment,…”
Score-Based Generative Modeling through Stochastic Differential Equations (2020, positive): “Crucially, this reverse process satisﬁes a reverse-time SDE (Anderson, 1982), which can be derived from the forward SDE given the score of the marginal probability densities as a function of time.”
Grad-StyleSpeech: Any-Speaker Adaptive Text-to-Speech Synthesis with Diffusion Models (2022, methodology): “Following the results from [19] and [6], reverse diffusion process of Equation 1 is given as the reverse-time SDE as follows [8]: where ˜ W t is a reverse Wiener process and ∇ Y t log p t ( Y t ) is the score function of the data distribution p t ( Y t ) .”
Guided-TTS: A Diffusion Model for Text-to-Speech via Classifier Guidance (2021, background): “Anderson (1982) shows that the reverse process, which represents the trajectory from noise XT to X0, can also be formulated in SDE, which is defined as follows: dXt = (− 1 2 Xt −∇Xt log pt(Xt))βtdt+ √ βtdW̃t, (2) where W̃t is a reverse-time Wiener process.”
Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speech (2021, methodology): “The result by Anderson (1982) implies that if n -dimensional process of the diffusion type X t satisﬁes dX t = f ( X t , t ) dt + g ( t ) dW t , t ∈ [0 , T ] , where g ( t ) is a function [0 , T ] → R , then its reverse-time dynamics is given by dX t = ( f ( X t , t ) − g 2 ( t ) ∇ log p t ( X t ))…”
Maximum Likelihood Training of Score-Based Diffusion Models (2021, methodology): “associated reverse-time diffusion process [1, 16] given by the following SDE dx “ “”
Gotta Go Fast When Generating Data with Score-Based Models (2021, background): “…this diffusion, drawing x (1) from its Gaussian distribution and solving the Reverse Diffusion Process (RDP) equal to: where ∇ x log p t ( x ) is referred to as the score of the distribution at time t [Hyvärinen, 2005] and ¯w ( t ) is the Wiener process in which time ﬂows backward [Anderson, 1982].”
A Variational Perspective on Diffusion-Based Generative Models and Score Matching (2021, background): “Time-reversal of diffusion processes Plenty of works have studied the reverse-time diffusion processes (2), including Anderson (1982); Föllmer (1985); Elliott & Anderson (1985); Haussmann & Pardoux (1986).”
Torsional Diffusion for Molecular Conformer Generation (2022, background): “Sampling from the prior and solving the reverse diffusion d x = f ( x t , t ) − g 2 ( t ) ∇ x log p t ( x ) dt + g ( t ) d ¯w (2) yields samples from the data distribution p 0 ( x ) [Anderson, 1982, Song et al., 2021].”
Diffusion Normalizing Flow (2021, methodology): “Our stochastic adjoint approach shares a similar spirit with SDE adjoint sensitivity [25].”
Universal Speech Enhancement with Score-based Diffusion (2022, methodology): “Sampling with score-based diffusion models is done by simulating or solving the reverse-time SDE (Eq.”
Denoising Diffusion Models for Plug-and-Play Image Restoration (2023, methodology): “The diffusion process described in (2) can be reversed in time and has the form of [2]: where p t ( x ) is the marginal probability density at timestep t , and the only unknown part ∇ x log p t ( x ) can be modelled as so-called score function s θ ( x , t ) with score matching methods [26, 52]. x…”
Non-Denoising Forward-Time Diffusions (2023, background): “As Y 0 ∼ P D , we have The dynamics of (1) over the reversed, i.e. sampling, time t = τ − r , t ∈ [0 , τ ] , are given by (Anderson, 1982; Haussmann & Pardoux, 1986; Millet et al., 1989) where r = τ − t is the remaining sampling time, G ( x, r ) = g ( x, r ) g ( x, r ) ⊤ and the D -dimensional and…”
Improving Diffusion Models for Inverse Problems using Manifold Constraints (2022, methodology): “The forward SDE in (1) is coupled with the following reverse SDE by the Anderson’s theorem [1, 41]: with dt denoting the inﬁnitesimal negative time step, and ¯ w deﬁning the standard Wiener process running backward in time.”
Speech Enhancement and Dereverberation With Diffusion-Based Generative Models (2022, unknown): “Our novel contribution lies in the modified drift term, by which the intended task adaptation is achieved. b) Reverse Process: Following Anderson [29] and Song et al. [28], the SDE in Eq.”
EdiTTS: Score-based Editing for Controllable Text-to-Speech (2021, methodology): “The reverse-time SDE [15] is given by ar X iv :2 11 0.”
Solving Inverse Problems in Medical Imaging with Score-Based Generative Models (2021, background): “(1) is given by the following reverse-time SDE [13, 14] dxt “ “”