Francisco Vargas

Francisco Vargas, Will Grathwohl, Arnaud Doucet

Denoising diffusion models are a popular class of generative models providing state-of-the-art results in many domains. One adds gradually noise to data using a diffusion to transform the data distribution into a Gaussian distribution. Samples from the generative model are then obtained by simulating an approximation of the time-reversal of this diffusion initialized by Gaussian samples. Practically, the intractable score terms appearing in the time-reversed process are approximated using score matching techniques. We explore here a similar idea to sample approximately from unnormalized probability density functions and estimate their normalizing constants. We consider a process where the target density diffuses towards a Gaussian. Denoising Diffusion Samplers (DDS) are obtained by approximating the corresponding time-reversal. While score matching is not applicable in this context, we can leverage many of the ideas introduced in generative modeling for Monte Carlo sampling. Existing theoretical results from denoising diffusion models also provide theoretical guarantees for DDS. We discuss the connections between DDS, optimal control and Schrödinger bridges and finally demonstrate DDS experimentally on a variety of challenging sampling tasks.

Aditya Ravuri, Francisco Vargas, Vidhi Lalchand et al. · cambridge

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation, noise reduction and efficient downstream processing of the data. In this work, we introduce the ProbDR variational framework, which interprets a wide range of classical DR algorithms as probabilistic inference algorithms in this framework. ProbDR encompasses PCA, CMDS, LLE, LE, MVU, diffusion maps, kPCA, Isomap, (t-)SNE, and UMAP. In our framework, a low-dimensional latent variable is used to construct a covariance, precision, or a graph Laplacian matrix, which can be used as part of a generative model for the data. Inference is done by optimizing an evidence lower bound. We demonstrate the internal consistency of our framework and show that it enables the use of probabilistic programming languages (PPLs) for DR. Additionally, we illustrate that the framework facilitates reasoning about unseen data and argue that our generative models approximate Gaussian processes (GPs) on manifolds. By providing a unified view of DR, our framework facilitates communication, reasoning about uncertainties, model composition, and extensions, particularly when domain knowledge is present.

Jiajun He, José Miguel Hernández-Lobato, Yuanqi Du et al. · cambridge

Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the \textit{density ratio} between path distributions, it reveals a fundamental connection between marginal densities and transition kernels, providing a flexible plug-and-play framework that unifies (1) diffusion density estimation, (2) inference-time control, and (3) energy-based diffusion training under a single perspective. Experiments demonstrate that RNE delivers strong results in inference-time control applications, such as annealing and model composition, with promising inference-time scaling performance, and achieves a simple yet efficient regularisation for training energy-based diffusion models. Additionally, our proposed RNE is modality-agnostic and applicable not only to continuous diffusion models but also to their discrete diffusion counterparts.

Jiajun He, Zijing Ou, Francisco Vargas et al.

Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. Recent work [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime. In this paper, we generalize this framework to arbitrary state spaces. Building on this view, we develop a generalized neural transport learning approach for efficient estimation. Experiments validate the effectiveness and efficiency of the proposed method beyond continuous settings, extending to discrete and multimodal spaces as well as autoregressive settings. Beyond free energy estimation, we establish algebraic identities and reveal a group-theoretic structure linking infinitesimal time reversal and generalized Doob's $h$-transforms, showing that their compositions form a generalized dihedral group.

Francisco Vargas, Shreyas Padhy, Denis Blessing et al.

Connecting optimal transport and variational inference, we present a principled and systematic framework for sampling and generative modelling centred around divergences on path space. Our work culminates in the development of the \emph{Controlled Monte Carlo Diffusion} sampler (CMCD) for Bayesian computation, a score-based annealing technique that crucially adapts both forward and backward dynamics in a diffusion model. On the way, we clarify the relationship between the EM-algorithm and iterative proportional fitting (IPF) for Schr{ö}dinger bridges, deriving as well a regularised objective that bypasses the iterative bottleneck of standard IPF-updates. Finally, we show that CMCD has a strong foundation in the Jarzinsky and Crooks identities from statistical physics, and that it convincingly outperforms competing approaches across a wide array of experiments.

Jiajun He, Yuanqi Du, Francisco Vargas et al. · cambridge

We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation -- a critical challenge across scientific domains. FEAT leverages learned transports implemented via stochastic interpolants and provides consistent, minimum-variance estimators based on escorted Jarzynski equality and controlled Crooks theorem, alongside variational upper and lower bounds on free energy differences. Unifying equilibrium and non-equilibrium methods under a single theoretical framework, FEAT establishes a principled foundation for neural free energy calculations. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods. Our PyTorch implementation is available at https://github.com/jiajunhe98/FEAT.

Riccardo Barbano, Alexander Denker, Zeljko Kereta et al.

Continuous-time generative models have achieved remarkable success in image restoration and synthesis. However, controlling the composition of multiple pre-trained models remains an open challenge. Current approaches largely treat composition as an algebraic composition of probability densities, such as via products or mixtures of experts. This perspective assumes the target distribution is known explicitly, which is almost never the case. In this work, we propose a different paradigm that formulates compositional generation as a cooperative Stochastic Optimal Control problem. Rather than combining probability densities, we treat pre-trained diffusion models as interacting agents whose diffusion trajectories are jointly steered, via optimal control, toward a shared objective defined on their aggregated output. We validate our framework on conditional MNIST generation and compare it against a naive inference-time DPS-style baseline replacing learned cooperative control with per-step gradient guidance.

Francisco Vargas, Alejandro González Coene, Gaston Escalante et al.

The extraction of information about traffic accidents from legal documents is crucial for quantifying insurance company costs. Extracting entities such as percentages of physical and/or psychological disability and the involved compensation amounts is a challenging process, even for experts, due to the subtle arguments and reasoning in the court decision. A two-step procedure is proposed: first, segmenting the document identifying the most relevant segments, and then extracting the entities. For text segmentation, two methodologies are compared: a classic method based on regular expressions and a second approach that divides the document into blocks of n-tokens, which are then vectorized using multilingual models for semantic searches (text-embedding-ada-002/MiniLM-L12-v2 ). Subsequently, large language models (LLaMA-2 7b, 70b, LLaMA-3 8b, and GPT-4 Turbo) are applied with prompting to the selected segments for entity extraction. For the LLaMA models, fine-tuning is performed using LoRA. LLaMA-2 7b, even with zero temperature, shows a significant number of hallucinations in extractions which are an important contention point for named entity extraction. This work shows that these hallucinations are substantially reduced after finetuning the model. The performance of the methodology based on segment vectorization and subsequent use of LLMs significantly surpasses the classic method which achieves an accuracy of 39.5%. Among open-source models, LLaMA-2 70B with finetuning achieves the highest accuracy 79.4%, surpassing its base version 61.7%. Notably, the base LLaMA-3 8B model already performs comparably to the finetuned LLaMA-2 70B model, achieving 76.6%, highlighting the rapid progress in model development. Meanwhile, GPT-4 Turbo achieves the highest accuracy at 86.1%.

Jiajun He, Yuanqi Du, Francisco Vargas et al. · cambridge

We consider the sampling problem, where the aim is to draw samples from a distribution whose density is known only up to a normalization constant. Recent breakthroughs in generative modeling to approximate a high-dimensional data distribution have sparked significant interest in developing neural network-based methods for this challenging problem. However, neural samplers typically incur heavy computational overhead due to simulating trajectories during training. This motivates the pursuit of simulation-free training procedures of neural samplers. In this work, we propose an elegant modification to previous methods, which allows simulation-free training with the help of a time-dependent normalizing flow. However, it ultimately suffers from severe mode collapse. On closer inspection, we find that nearly all successful neural samplers rely on Langevin preconditioning to avoid mode collapsing. We systematically analyze several popular methods with various objective functions and demonstrate that, in the absence of Langevin preconditioning, most of them fail to adequately cover even a simple target. Finally, we draw attention to a strong baseline by combining the state-of-the-art MCMC method, Parallel Tempering (PT), with an additional generative model to shed light on future explorations of neural samplers.

Kieran Didi, Francisco Vargas, Simon V Mathis et al. · cambridge

Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address this motif scaffolding problem and have shown early experimental success in some cases. In the diffusion paradigm, motif scaffolding is treated as a conditional generation task, and several conditional generation protocols were proposed or imported from the Computer Vision literature. However, most of these protocols are motivated heuristically, e.g. via analogies to Langevin dynamics, and lack a unifying framework, obscuring connections between the different approaches. In this work, we unify conditional training and conditional sampling procedures under one common framework based on the mathematically well-understood Doob's h-transform. This new perspective allows us to draw connections between existing methods and propose a new variation on existing conditional training protocols. We illustrate the effectiveness of this new protocol in both, image outpainting and motif scaffolding and find that it outperforms standard methods.

Cheuk Kit Lee, Paul Jeha, Jes Frellsen et al.

Discrete diffusion models are a class of generative models that produce samples from an approximated data distribution within a discrete state space. Often, there is a need to target specific regions of the data distribution. Current guidance methods aim to sample from a distribution with mass proportional to $p_0(x_0) p(ζ|x_0)^α$ but fail to achieve this in practice. We introduce a Sequential Monte Carlo algorithm that generates unbiasedly from this target distribution, utilising the learnt unconditional and guided process. We validate our approach on low-dimensional distributions, controlled images and text generations. For text generation, our method provides strong control while maintaining low perplexity compared to guidance-based approaches.

Leo Zhang, Peter Potaptchik, Jiajun He et al. · cambridge

Markov Chain Monte Carlo (MCMC) algorithms are essential tools in computational statistics for sampling from unnormalised probability distributions, but can be fragile when targeting high-dimensional, multimodal, or complex target distributions. Parallel Tempering (PT) enhances MCMC's sample efficiency through annealing and parallel computation, propagating samples from tractable reference distributions to intractable targets via state swapping across interpolating distributions. The effectiveness of PT is limited by the often minimal overlap between adjacent distributions in challenging problems, which requires increasing the computational resources to compensate. We introduce a framework that accelerates PT by leveraging neural samplers -- including normalising flows, diffusion models, and controlled diffusions -- to reduce the required overlap. Our approach utilises neural samplers in parallel, circumventing the computational burden of neural samplers while preserving the asymptotic consistency of classical PT. We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality, reduces the computational cost compared to classical PT, and enables efficient free energy/normalising constant estimation.

Alexander Denker, Shreyas Padhy, Francisco Vargas et al.

Diffusion models are an important tool for generative modelling, serving as effective priors in applications such as imaging and protein design. A key challenge in applying diffusion models for downstream tasks is efficiently sampling from resulting posterior distributions, which can be addressed using the $h$-transform. This work introduces a self-supervised algorithm for fine-tuning diffusion models by estimating the $h$-transform, enabling amortised conditional sampling. Our method iteratively refines the $h$-transform using a synthetic dataset resampled with path-based importance weights. We demonstrate the effectiveness of this framework on class-conditional sampling, inverse problems and reward fine-tuning for text-to-image diffusion models.

Sergei Kholkin, Francisco Vargas, Alexander Korotin

We introduce the Target Concrete Score Identity Sampler (TCSIS), a method for sampling from unnormalized densities on discrete state spaces by learning the reverse dynamics of a Continuous-Time Markov Chain (CTMC). Our approach builds on a forward in time CTMC with a uniform noising kernel and relies on the proposed Target Concrete Score Identity, which relates the concrete score, the ratio of marginal probabilities of two states, to a ratio of expectations of Boltzmann factors under the forward uniform diffusion kernel. This formulation enables Monte Carlo estimation of the concrete score without requiring samples from the target distribution or computation of the partition function. We approximate the concrete score with a neural network and propose two algorithms: Self-Normalized TCSIS and Unbiased TCSIS. Finally, we demonstrate the effectiveness of TCSIS on problems from statistical physics.

Teodora Reu, Sixtine Dromigny, Michael Bronstein et al.

Rectified Flows learn ODE vector fields whose trajectories are straight between source and target distributions, enabling near one-step inference. We show that this straight-path objective conceals fundamental failure modes: under deterministic training, low gradient variance drives memorization of arbitrary training pairings, even when interpolant lines between pairs intersect. To analyze this mechanism, we study Gaussian-to-Gaussian transport and use the loss gradient variance across stochastic and deterministic regimes to characterize which vector fields optimization favors in each setting. We then show that, in a setting where all interpolating lines intersect, applying Rectified Flow yields the same specific pairings at inference as during training. More generally, we prove that a memorizing vector field exists even when training interpolants intersect, and that optimizing the straight-path objective converges to this ill-defined field. At inference, deterministic integration reproduces the exact training pairings. We validate our findings empirically on the CelebA dataset, confirming that deterministic interpolants induce memorization, while the injection of small noise restores generalization.

Jiajun He, Paul Jeha, Peter Potaptchik et al. · cambridge

Inference-time control of diffusion models aims to steer model outputs to satisfy new constraints without retraining. Previous approaches have mostly relied on heuristic guidance or have been coupled with Sequential Monte Carlo (SMC) for bias correction. In this paper, we propose a flexible alternative based on replica exchange, an algorithm designed initially for sampling problems. We refer to this method as the CREPE (Controlling with REPlica Exchange). Unlike SMC, CREPE: (1) generates particles sequentially, (2) maintains high diversity in the generated samples after a burn-in period, and (3) enables online refinement or early termination. We demonstrate its versatility across various tasks, including temperature annealing, reward-tilting, model composition and classifier-free guidance debiasing, with competitive performance compared to prior SMC methods.

Denis Blessing, Xiaogang Jia, Johannes Esslinger et al.

Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance measures and limited method comparisons across diverse tasks, complicating the assessment of progress and hindering the decision-making of practitioners. In response to these challenges, our work introduces a benchmark that evaluates sampling methods using a standardized task suite and a broad range of performance criteria. Moreover, we study existing metrics for quantifying mode collapse and introduce novel metrics for this purpose. Our findings provide insights into strengths and weaknesses of existing sampling methods, serving as a valuable reference for future developments. The code is publicly available here.

Paulina Kulytė, Francisco Vargas, Simon Valentin Mathis et al.

Antibodies, crucial for immune defense, primarily rely on complementarity-determining regions (CDRs) to bind and neutralize antigens, such as viruses. The design of these CDRs determines the antibody's affinity and specificity towards its target. Generative models, particularly denoising diffusion probabilistic models (DDPMs), have shown potential to advance the structure-based design of CDR regions. However, only a limited dataset of bound antibody-antigen structures is available, and generalization to out-of-distribution interfaces remains a challenge. Physics based force-fields, which approximate atomic interactions, offer a coarse but universal source of information to better mold designs to target interfaces. Integrating this foundational information into diffusion models is, therefore, highly desirable. Here, we propose a novel approach to enhance the sampling process of diffusion models by integrating force field energy-based feedback. Our model, DiffForce, employs forces to guide the diffusion sampling process, effectively blending the two distributions. Through extensive experiments, we demonstrate that our method guides the model to sample CDRs with lower energy, enhancing both the structure and sequence of the generated antibodies.

Alexander Denker, Francisco Vargas, Shreyas Padhy et al.

Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images. Further, we also provide initial experiments on protein motif scaffolding and outperform reconstruction guidance methods.

Francisco Vargas, Teodora Reu, Anna Kerekes et al.

Denoising diffusion models are a class of generative models which have recently achieved state-of-the-art results across many domains. Gradual noise is added to the data using a diffusion process, which transforms the data distribution into a Gaussian. Samples from the generative model are then obtained by simulating an approximation of the time reversal of this diffusion initialized by Gaussian samples. Recent research has explored adapting diffusion models for sampling and inference tasks. In this paper, we leverage known connections to stochastic control akin to the Föllmer drift to extend established neural network approximation results for the Föllmer drift to denoising diffusion models and samplers.

Shauli Ravfogel, Francisco Vargas, Yoav Goldberg et al.

The representation space of neural models for textual data emerges in an unsupervised manner during training. Understanding how those representations encode human-interpretable concepts is a fundamental problem. One prominent approach for the identification of concepts in neural representations is searching for a linear subspace whose erasure prevents the prediction of the concept from the representations. However, while many linear erasure algorithms are tractable and interpretable, neural networks do not necessarily represent concepts in a linear manner. To identify non-linearly encoded concepts, we propose a kernelization of a linear minimax game for concept erasure. We demonstrate that it is possible to prevent specific non-linear adversaries from predicting the concept. However, the protection does not transfer to different nonlinear adversaries. Therefore, exhaustively erasing a non-linearly encoded concept remains an open problem.

Francisco Vargas, Andrius Ovsianas, David Fernandes et al.

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control (i.e. Schrödinger bridges). We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics (SGLD). Furthermore, we discuss and adapt the existing theoretical guarantees of this framework and establish connections to already existing VI routines in SDE-based models.

Han Xuanyuan, Francisco Vargas, Stephen Cummins

The processing of sensitive user data using deep learning models is an area that has gained recent traction. Existing work has leveraged homomorphic encryption (HE) schemes to enable computation on encrypted data. An early work was CryptoNets, which takes 250 seconds for one MNIST inference. The main limitation of such approaches is that of the expensive FFT-like operations required to perform operations on HE-encrypted ciphertext. Others have proposed the use of model pruning and efficient data representations to reduce the number of HE operations required. We focus on improving upon existing work by proposing changes to the representations of intermediate tensors during CNN inference. We construct and evaluate private CNNs on the MNIST and CIFAR-10 datasets, and achieve over a two-fold reduction in the number of operations used for inferences of the CryptoNets architecture.

Francisco Vargas, Pierre Thodoroff, Neil D. Lawrence et al.

The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. We prove an equivalence between the SBP and maximum likelihood estimation enabling direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.

Francisco Vargas, Ryan Cotterell

Bolukbasi et al. (2016) presents one of the first gender bias mitigation techniques for word representations. Their method takes pre-trained word representations as input and attempts to isolate a linear subspace that captures most of the gender bias in the representations. As judged by an analogical evaluation task, their method virtually eliminates gender bias in the representations. However, an implicit and untested assumption of their method is that the bias subspace is actually linear. In this work, we generalize their method to a kernelized, nonlinear version. We take inspiration from kernel principal component analysis and derive a nonlinear bias isolation technique. We discuss and overcome some of the practical drawbacks of our method for non-linear gender bias mitigation in word representations and analyze empirically whether the bias subspace is actually linear. Our analysis shows that gender bias is in fact well captured by a linear subspace, justifying the assumption of Bolukbasi et al. (2016).

Francisco Vargas, Kamen Brestnichki, Alex Papadopoulos-Korfiatis et al.

In this work we approach the task of learning multilingual word representations in an offline manner by fitting a generative latent variable model to a multilingual dictionary. We model equivalent words in different languages as different views of the same word generated by a common latent variable representing their latent lexical meaning. We explore the task of alignment by querying the fitted model for multilingual embeddings achieving competitive results across a variety of tasks. The proposed model is robust to noise in the embedding space making it a suitable method for distributed representations learned from noisy corpora.

Francisco Vargas, Kamen Brestnichki, Nils Hammerla

We introduce a probabilistic framework for quantifying the semantic similarity between two groups of embeddings. We formulate the task of semantic similarity as a model comparison task in which we contrast a generative model which jointly models two sentences versus one that does not. We illustrate how this framework can be used for the Semantic Textual Similarity tasks using clear assumptions about how the embeddings of words are generated. We apply model comparison that utilises information criteria to address some of the shortcomings of Bayesian model comparison, whilst still penalising model complexity. We achieve competitive results by applying the proposed framework with an appropriate choice of likelihood on the STS datasets.

Alexander Gomez, Augusto Salazar, Francisco Vargas

Non intrusive monitoring of animals in the wild is possible using camera trapping framework, which uses cameras triggered by sensors to take a burst of images of animals in their habitat. However camera trapping framework produces a high volume of data (in the order on thousands or millions of images), which must be analyzed by a human expert. In this work, a method for animal species identification in the wild using very deep convolutional neural networks is presented. Multiple versions of the Snapshot Serengeti dataset were used in order to probe the ability of the method to cope with different challenges that camera-trap images demand. The method reached 88.9% of accuracy in Top-1 and 98.1% in Top-5 in the evaluation set using a residual network topology. Also, the results show that the proposed method outperforms previous approximations and proves that recognition in camera-trap images can be automated.

Carlos Palma, Augusto Salazar, Francisco Vargas

Automatic recognition of the quality of movement in human beings is a challenging task, given the difficulty both in defining the constraints that make a movement correct, and the difficulty in using noisy data to determine if these constraints were satisfied. This paper presents a method for the detection of deviations from the correct form in movements from physical therapy routines based on Hidden Markov Models, which is compared to Dynamic Time Warping. The activities studied include upper an lower limbs movements, the data used comes from a Kinect sensor. Correct repetitions of the activities of interest were recorded, as well as deviations from these correct forms. The ability of the proposed approach to detect these deviations was studied. Results show that a system based on HMM is much more likely to determine if a certain movement has deviated from the specification.