Joaquín Fontbona

Camilo Carvajal Reyes, Joaquín Fontbona, Felipe Tobar

Score-based generative models (SBM), also known as diffusion models, are the de facto state of the art for image synthesis. Despite their unparalleled performance, SBMs have recently been in the spotlight for being tricked into creating not-safe-for-work (NSFW) content, such as violent images and non-consensual nudity. Current approaches that prevent unsafe generation are based on the models' own knowledge, and the majority of them require fine-tuning. This article explores the use of external sources for ensuring safe outputs in SBMs. Our safe-for-work (SFW) sampler implements a Conditional Trajectory Correction step that guides the samples away from undesired regions in the ambient space using multimodal models as the source of conditioning. Furthermore, using Contrastive Language Image Pre-training (CLIP), our method admits user-defined NSFW classes, which can vary in different settings. Our experiments on the text-to-image SBM Stable Diffusion validate that the proposed SFW sampler effectively reduces the generation of explicit content while being competitive with other fine-tuning-based approaches, as assessed via independent NSFW detectors. Moreover, we evaluate the impact of the SFW sampler on image quality and show that the proposed correction scheme comes at a minor cost with negligible effect on samples not needing correction. Our study confirms the suitability of the SFW sampler towards aligned SBM models and the potential of using model-agnostic conditioning for the prevention of unwanted images.

Elsa Cazelles, Felipe Tobar, Joaquín Fontbona

We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical analysis of this object and discuss its interpretation in the light of convex ordering between probability measures. In particular, we show that, rather than averaging the input distributions in a geometric way (as the Wasserstein barycenter based on classic optimal transport does) weak barycenters extract common geometric information shared by all the input distributions, encoded as a latent random variable that underlies all of them. We also provide an iterative algorithm to compute a weak barycenter for a finite family of input distributions, and a stochastic algorithm that computes them for arbitrary populations of laws. The latter approach is particularly well suited for the streaming setting, i.e., when distributions are observed sequentially. The notion of weak barycenter and our approaches to compute it are illustrated on synthetic examples, validated on 2D real-world data and compared to standard Wasserstein barycenters.

Julio Backhoff-Veraguas, Joaquin Fontbona, Gonzalo Rios et al.

We introduce and study a novel model-selection strategy for Bayesian learning, based on optimal transport, along with its associated predictive posterior law: the Wasserstein population barycenter of the posterior law over models. We first show how this estimator, termed Bayesian Wasserstein barycenter (BWB), arises naturally in a general, parameter-free Bayesian model-selection framework, when the considered Bayesian risk is the Wasserstein distance. Examples are given, illustrating how the BWB extends some classic parametric and non-parametric selection strategies. Furthermore, we also provide explicit conditions granting the existence and statistical consistency of the BWB, and discuss some of its general and specific properties, providing insights into its advantages compared to usual choices, such as the model average estimator. Finally, we illustrate how this estimator can be computed using the stochastic gradient descent (SGD) algorithm in Wasserstein space introduced in a companion paper arXiv:2201.04232v2 [math.OC], and provide a numerical example for experimental validation of the proposed method.