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Wavelet Score-Based Generative Modeling [article]

Florentin Guth, Simon Coste, Valentin De Bortoli, Stephane Mallat
2022 arXiv   pre-print
We recall the following result from (De Bortoli et al., 2021, Theorem 1) . Theorem 22.  ...  The beginning of the proof is similar to the one of (De Bortoli et al., 2021, Theorem 1) .  ...  Using Lemma 23 and Lemma 25, we have that for any t ∈ [0, T ] Combining this result and (De Bortoli et al., 2021, Lemma S13) we have that Therefore, we get that which concludes the proof upon using Lemma  ... 
arXiv:2208.05003v1 fatcat:jlojnogsqbaodn32szkzduebcy

Macrocanonical Models for Texture Synthesis [article]

De Bortoli Valentin, Desolneux Agnès, Galerne Bruno, Leclaire Arthur
2019 arXiv   pre-print
In this article we consider macrocanonical models for texture synthesis. In these models samples are generated given an input texture image and a set of features which should be matched in expectation. It is known that if the images are quantized, macrocanonical models are given by Gibbs measures, using the maximum entropy principle. We study conditions under which this result extends to real-valued images. If these conditions hold, finding a macrocanonical model amounts to minimizing a convex
more » ... unction and sampling from an associated Gibbs measure. We analyze an algorithm which alternates between sampling and minimizing. We present experiments with neural network features and study the drawbacks and advantages of using this sampling scheme.
arXiv:1904.06396v1 fatcat:u2kjc74icje7tdjraotvximyem

Convergence of denoising diffusion models under the manifold hypothesis [article]

Valentin De Bortoli
2022 arXiv   pre-print
Contrary to De Bortoli et al. (2021); Lee et al. (2022); associated discrete process (Y EM k ) k∈{0,...  ...  In particular, De Bortoli et al. ( 2022 ) focus on manifolds which have a well-known structure such as S 1 , T 2 or SO 3 (R).  ... 
arXiv:2208.05314v1 fatcat:hqg3vhfcpvalfhn4uvwo6kbiqq

Simulating Diffusion Bridges with Score Matching [article]

Valentin De Bortoli, Arnaud Doucet, Jeremy Heng, James Thornton
2021 arXiv   pre-print
Acknowledgements Valentin De Bortoli and Arnaud Doucet are partly supported by the EPSRC grant CoSInES EP/R034710/1.  ...  This was motivated by our recent work in De Bortoli et al. ( 2021 ) on a related but distinct problem of simulating Schrödinger bridges.  ... 
arXiv:2111.07243v1 fatcat:ubtfb6x27veb7lm46pl2y7hddm

Riemannian Diffusion Schrödinger Bridge [article]

James Thornton, Michael Hutchinson, Emile Mathieu, Valentin De Bortoli, Yee Whye Teh, Arnaud Doucet
2022 arXiv   pre-print
Other experimental details follow De Bortoli et al. (2022).  ...  Similar results hold for the Schrödinger Bridge (De Bortoli et al., 2021; Chen et al., 2022) and in the Riemannian setting (De Bortoli et al., 2022) .  ... 
arXiv:2207.03024v1 fatcat:rdeza3l6ynbyzje7tvqctrgny4

Can Push-forward Generative Models Fit Multimodal Distributions? [article]

Antoine Salmona, Valentin de Bortoli, Julie Delon, Agnès Desolneux
2022 arXiv   pre-print
Many generative models synthesize data by transforming a standard Gaussian random variable using a deterministic neural network. Among these models are the Variational Autoencoders and the Generative Adversarial Networks. In this work, we call them "push-forward" models and study their expressivity. We show that the Lipschitz constant of these generative networks has to be large in order to fit multimodal distributions. More precisely, we show that the total variation distance and the
more » ... eibler divergence between the generated and the data distribution are bounded from below by a constant depending on the mode separation and the Lipschitz constant. Since constraining the Lipschitz constants of neural networks is a common way to stabilize generative models, there is a provable trade-off between the ability of push-forward models to approximate multimodal distributions and the stability of their training. We validate our findings on one-dimensional and image datasets and empirically show that generative models consisting of stacked networks with stochastic input at each step, such as diffusion models do not suffer of such limitations.
arXiv:2206.14476v1 fatcat:qeikzoqh5nhz7cda5jsb3xelge

A Continuous Time Framework for Discrete Denoising Models [article]

Andrew Campbell, Joe Benton, Valentin De Bortoli, Tom Rainforth, George Deligiannidis, Arnaud Doucet
2022 arXiv   pre-print
We provide the first complete continuous time framework for denoising diffusion models of discrete data. This is achieved by formulating the forward noising process and corresponding reverse time generative process as Continuous Time Markov Chains (CTMCs). The model can be efficiently trained using a continuous time version of the ELBO. We simulate the high dimensional CTMC using techniques developed in chemical physics and exploit our continuous time framework to derive high performance
more » ... s that we show can outperform discrete time methods for discrete data. The continuous time treatment also enables us to derive a novel theoretical result bounding the error between the generated sample distribution and the true data distribution.
arXiv:2205.14987v1 fatcat:kexw76ned5axxadtze6fynu4i4

Conditional Simulation Using Diffusion Schrödinger Bridges [article]

Yuyang Shi, Valentin De Bortoli, George Deligiannidis, Arnaud Doucet
2022 arXiv   pre-print
The proof of this proposition is a straightforward extension of [De Bortoli et al., 2021, Proposition 6] .  ...  The same strategy can be applied to both DSB and CDSB; see [De Bortoli et al., 2021, Section H.3] for details for DSB.  ...  The following results are a generalization to the conditional framework of the continuous-time results of De Bortoli et al. [2021] .  ... 
arXiv:2202.13460v2 fatcat:c2tlq7f72ff6lfn4uz4qanakzq

Macrocanonical Models for Texture Synthesis [chapter]

Valentin De Bortoli, Agnès Desolneux, Bruno Galerne, Arthur Leclaire
2019 Lecture Notes in Computer Science  
In this article we consider macrocanonical models for texture synthesis. In these models samples are generated given an input texture image and a set of features which should be matched in expectation. It is known that if the images are quantized, macrocanonical models are given by Gibbs measures, using the maximum entropy principle. We study conditions under which this result extends to real-valued images. If these conditions hold, finding a macrocanonical model amounts to minimizing a convex
more » ... unction and sampling from an associated Gibbs measure. We analyze an algorithm which alternates between sampling and minimizing. We present experiments with neural network features and study the drawbacks and advantages of using this sampling scheme.
doi:10.1007/978-3-030-22368-7_2 fatcat:pjroxfpiova5dip5orrafrdm5a

Riemannian Score-Based Generative Modeling [article]

Valentin De Bortoli, Emile Mathieu, Michael Hutchinson, James Thornton, Yee Whye Teh, Arnaud Doucet
2022 arXiv   pre-print
However, in order for the method to yield good results we need L(Y 0 ) ≈ L(X T ) (see De Bortoli et al., 2021, Theorem 1) .  ...  Another promising extension concerns stochastic control on manifolds and more precisely, deriving efficient algorithms to solve Schrödinger bridges in the same spirit as De Bortoli et al. (2021) Watson  ... 
arXiv:2202.02763v2 fatcat:zs2tqvqj4ffg7lq6hzpewvzdw4

Patch redundancy in images: a statistical testing framework and some applications [article]

De Bortoli Valentin, Desolneux Agnès, Galerne Bruno, Leclaire Arthur
2019 arXiv   pre-print
In this work we introduce a statistical framework in order to analyze the spatial redundancy in natural images. This notion of spatial redundancy must be defined locally and thus we give some examples of functions (auto-similarity and template similarity) which, given one or two images, computes a similarity measurement between patches. Two patches are said to be similar if the similarity measurement is small enough. To derive a criterion for taking a decision on the similarity between two
more » ... es we present an a contrario model. Namely, two patches are said to be similar if the associated similarity measurement is unlikely to happen in a background model. Choosing Gaussian random fields as background models we derive non-asymptotic expressions for the probability distribution function of similarity measurements. We introduce a fast algorithm in order to assess redundancy in natural images and present applications in denoising, periodicity analysis and texture ranking.
arXiv:1904.06428v1 fatcat:35jn4vkl4jdltjhpo4n2dpsho4

Maximum entropy methods for texture synthesis: theory and practice [article]

Valentin De Bortoli and Agnes Desolneux and Alain Durmus and Bruno Galerne and Arthur Leclaire
2019 arXiv   pre-print
De Bortoli and A. Durmus, Convergence of diffusions and their discretizations: from continuous to discrete processes and back, 2019, https://arxiv.org/abs/1904. 09808. [26] V. De Bortoli, A.  ... 
arXiv:1912.01691v1 fatcat:2xy6eoauujaipo4hwzvtsv2rpm

Redundancy in Gaussian random fields

Valentin DE BORTOLI, Agnès Desolneux, Bruno Galerne, Arthur Leclaire
2020 E S A I M: Probability & Statistics  
We introduce and study a notion of spatial redundancy in Gaussian random fields. we define similarity functions with some properties and give insight about their statistical properties in the context of image processing. We compute these similarity functions on local windows in random fields defined over discrete or continuous domains. We give explicit asymptotic Gaussian expressions for the distribution of similarity function random variables when computed over Gaussian random fields and
more » ... rate the weaknesses of such Gaussian approximations by showing that the approximated probability of rare events is not precise enough, even for large windows. In the special case of the squared $L^2$ norm, non-asymptotic expressions are derived in both discrete and continuous periodic settings. A fast and accurate approximation is introduced using eigenvalues projection and moment methods.
doi:10.1051/ps/2020010 fatcat:53u6wuu2gvafdk2xj5txcnircm

Solving Fredholm Integral Equations of the First Kind via Wasserstein Gradient Flows [article]

Francesca R. Crucinio, Valentin De Bortoli, Arnaud Doucet, Adam M. Johansen
2022 arXiv   pre-print
We investigate the long-time behaviour of these MKVS-DEs in the context of the minimization of G η α in Section 3.2.  ... 
arXiv:2209.09936v1 fatcat:v3zmeabijnd5xd25mremscqs54

Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure [article]

George Deligiannidis, Valentin De Bortoli, Arnaud Doucet
2021 arXiv   pre-print
Bernton et al. (2019) ; Chen et al. (2021) ; Corenflos et al. (2021); De Bortoli et al. (2021) ; Huang et al. (2021) ; Li et al. (2020) ; Vargas et al. (2021) .  ... 
arXiv:2108.08129v2 fatcat:5q25adnjtrajrnlioactng34re
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