Kyriakos Flouris

Gustav Bredell, Kyriakos Flouris, Krishna Chaitanya et al.

Variational autoencoders (VAEs) are powerful generative modelling methods, however they suffer from blurry generated samples and reconstructions compared to the images they have been trained on. Significant research effort has been spent to increase the generative capabilities by creating more flexible models but often flexibility comes at the cost of higher complexity and computational cost. Several works have focused on altering the reconstruction term of the evidence lower bound (ELBO), however, often at the expense of losing the mathematical link to maximizing the likelihood of the samples under the modeled distribution. Here we propose a new formulation of the reconstruction term for the VAE that specifically penalizes the generation of blurry images while at the same time still maximizing the ELBO under the modeled distribution. We show the potential of the proposed loss on three different data sets, where it outperforms several recently proposed reconstruction losses for VAEs.

Kyriakos Flouris, Ender Konukoglu

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an efficient representation of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.

Haichao Wang, Alexander Okupnik, Yuxing Han et al.

Long-range human movement generation remains a central challenge in computer vision and graphics. Generating coherent transitions across semantically distinct motion domains remains largely unexplored. This capability is particularly important for applications such as dance choreography, where movements must fluidly transition across diverse stylistic and semantic motifs. We propose a simple and effective inference-time optimization framework inspired by diffusion-based stochastic optimal control. Specifically, a control-energy objective that explicitly regularizes the transition trajectories of a pretrained diffusion model. We show that optimizing this objective at inference time yields transitions with fidelity and temporal coherence. This is the first work to provide a general framework for controlled long-range human motion generation with explicit transition modeling.

Kyriakos Flouris, Anna Volokitin, Gustav Bredell et al.

The autoencoder model typically uses an encoder to map data to a lower dimensional latent space and a decoder to reconstruct it. However, relying on an encoder for inversion can lead to suboptimal representations, particularly limiting in physical sciences where precision is key. We introduce a decoder-only method using gradient flow to directly encode data into the latent space, defined by ordinary differential equations (ODEs). This approach eliminates the need for approximate encoder inversion. We train the decoder via the adjoint method and show that costly integrals can be avoided with minimal accuracy loss. Additionally, we propose a $2^{nd}$ order ODE variant, approximating Nesterov's accelerated gradient descent for faster convergence. To handle stiff ODEs, we use an adaptive solver that prioritizes loss minimization, improving robustness. Compared to traditional autoencoders, our method demonstrates explicit encoding and superior data efficiency, which is crucial for data-scarce scenarios in the physical sciences. Furthermore, this work paves the way for integrating machine learning into scientific workflows, where precise and efficient encoding is critical. \footnote{The code for this work is available at \url{https://github.com/k-flouris/gfe}.}

Mohammadreza Amirian, Michael Bach, Oscar Jimenez-del-Toro et al.

Artificial intelligence (AI) has introduced numerous opportunities for human assistance and task automation in medicine. However, it suffers from poor generalization in the presence of shifts in the data distribution. In the context of AI-based computed tomography (CT) analysis, significant data distribution shifts can be caused by changes in scanner manufacturer, reconstruction technique or dose. AI harmonization techniques can address this problem by reducing distribution shifts caused by various acquisition settings. This paper presents an open-source benchmark dataset containing CT scans of an anthropomorphic phantom acquired with various scanners and settings, which purpose is to foster the development of AI harmonization techniques. Using a phantom allows fixing variations attributed to inter- and intra-patient variations. The dataset includes 1378 image series acquired with 13 scanners from 4 manufacturers across 8 institutions using a harmonized protocol as well as several acquisition doses. Additionally, we present a methodology, baseline results and open-source code to assess image- and feature-level stability and liver tissue classification, promoting the development of AI harmonization strategies.

Kyriakos Flouris, Moritz Halter, Yolanne Y. R. Lee et al.

Hemodynamic analysis is essential for predicting aneurysm rupture and guiding treatment. While magnetic resonance flow imaging enables time-resolved volumetric blood velocity measurements, its low spatiotemporal resolution and signal-to-noise ratio limit its diagnostic utility. To address this, we propose the Localized Fourier Neural Operator (LoFNO), a novel 3D architecture that enhances both spatial and temporal resolution with the ability to predict wall shear stress (WSS) directly from clinical imaging data. LoFNO integrates Laplacian eigenvectors as geometric priors for improved structural awareness on irregular, unseen geometries and employs an Enhanced Deep Super-Resolution Network (EDSR) layer for robust upsampling. By combining geometric priors with neural operator frameworks, LoFNO de-noises and spatiotemporally upsamples flow data, achieving superior velocity and WSS predictions compared to interpolation and alternative deep learning methods, enabling more precise cerebrovascular diagnostics.

Yanke Wang, Yolanne Y. R. Lee, Aurelio Dolfini et al.

Lumbar spine problems are ubiquitous, motivating research into targeted imaging for treatment planning and guided interventions. While high resolution and high contrast CT has been the modality of choice, MRI can capture both bone and soft tissue without the ionizing radiation of CT albeit longer acquisition time. The critical trade-off between contrast quality and acquisition time has motivated 'thick slice MRI', which prioritises faster imaging with high in-plane resolution but variable contrast and low through-plane resolution. We investigate a recently developed post-acquisition pipeline which segments vertebrae from thick-slice acquisitions and uses a variational autoencoder to enhance quality after an initial 3D reconstruction. We instead propose a latent space diffusion energy-based prior to leverage diffusion models, which exhibit high-quality image generation. Crucially, we mitigate their high computational cost and low sample efficiency by learning an energy-based latent representation to perform the diffusion processes. Our resulting method outperforms existing approaches across metrics including Dice and VS scores, and more faithfully captures 3D features.

Yolanne Yi Ran Lee, Kyriakos Flouris

Forecasting high-dimensional, PDE-governed dynamics remains a core challenge for generative modeling. Existing autoregressive and diffusion-based approaches often suffer cumulative errors and discretisation artifacts that limit long, physically consistent forecasts. Flow matching offers a natural alternative, enabling efficient, deterministic sampling. We prove an upper bound on FNO approximation error and propose TempO, a latent flow matching model leveraging sparse conditioning with channel folding to efficiently process 3D spatiotemporal fields using time-conditioned Fourier layers to capture multi-scale modes with high fidelity. TempO outperforms state-of-the-art baselines across three benchmark PDE datasets, and spectral analysis further demonstrates superior recovery of multi-scale dynamics, while efficiency studies highlight its parameter- and memory-light design compared to attention-based or convolutional regressors.

Alexander Okupnik, Johannes Schneider, Kyriakos Flouris

Recent success with large language models has sparked a new wave of verbal human-AI interaction. While such models support users in a variety of creative tasks, they lack the embodied nature of human interaction. Dance, as a primal form of human expression, is predestined to complement this experience. To explore creative human-AI interaction exemplified by dance, we build an interactive model based on motion capture (MoCap) data. It generates an artificial other by partially mimicking and also "creatively" enhancing an incoming sequence of movement data. It is the first model, which leverages single-person motion data and high level features in order to do so and, thus, it does not rely on low level human-human interaction data. It combines ideas of two diffusion models, motion inpainting, and motion style transfer to generate movement representations that are both temporally coherent and responsive to a chosen movement reference. The success of the model is demonstrated by quantitatively assessing the convergence of the feature distribution of the generated samples and the test set which serves as simulating the human performer. We show that our generations are first steps to creative dancing with AI as they are both diverse showing various deviations from the human partner while appearing realistic.

Yanke Wang, Kyriakos Flouris

This work explores optimization methods on hyperbolic manifolds. Building on Riemannian optimization principles, we extend the Hyperbolic Stochastic Gradient Descent (a specialization of Riemannian SGD) to a Hyperbolic Adam optimizer. While these methods are particularly relevant for learning on the Poincaré ball, they may also provide benefits in Euclidean and other non-Euclidean settings, as the chosen optimization encourages the learning of Poincaré embeddings. This representation, in turn, accelerates convergence in the early stages of training, when parameters are far from the optimum. As a case study, we train diffusion models using the hyperbolic optimization methods with hyperbolic time-discretization of the Langevin dynamics, and show that they achieve faster convergence on certain datasets without sacrificing generative quality.

Alex Mossi, Bojan Žunkovic, Kyriakos Flouris

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These networks are used to approximate high-order tensors by contracting tensors with lower ranks. Initially developed for simulating quantum systems, tensor networks have become integral to quantum computing and, by extension, to QML. Drawing inspiration from these quantum methods, specifically the Matrix Product States (MPS), we apply them in a classical machine learning setting. Their ability to efficiently represent and manipulate complex, high-dimensional data makes them effective in a supervised learning framework. Here, we present an MPS model, in which the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model permits a strategy that enhances the traditional training of supervised MPS models. This framework is inspired by generative adversarial networks and is geared towards generating more realistic samples by reducing outliers. In addition, our contributions offer insights into the mechanics of tensor network methods for generation tasks. Specifically, we discuss alternative embedding functions and a new sampling method from non-normalized MPSs.

Kyriakos Flouris, Anna Volokitin, Gustav Bredell et al.

The autoencoder model uses an encoder to map data samples to a lower dimensional latent space and then a decoder to map the latent space representations back to the data space. Implicitly, it relies on the encoder to approximate the inverse of the decoder network, so that samples can be mapped to and back from the latent space faithfully. This approximation may lead to sub-optimal latent space representations. In this work, we investigate a decoder-only method that uses gradient flow to encode data samples in the latent space. The gradient flow is defined based on a given decoder and aims to find the optimal latent space representation for any given sample through optimisation, eliminating the need of an approximate inversion through an encoder. Implementing gradient flow through ordinary differential equations (ODE), we leverage the adjoint method to train a given decoder. We further show empirically that the costly integrals in the adjoint method may not be entirely necessary. Additionally, we propose a $2^{nd}$ order ODE variant to the method, which approximates Nesterov's accelerated gradient descent, with faster convergence per iteration. Commonly used ODE solvers can be quite sensitive to the integration step-size depending on the stiffness of the ODE. To overcome the sensitivity for gradient flow encoding, we use an adaptive solver that prioritises minimising loss at each integration step. We assess the proposed method in comparison to the autoencoding model. In our experiments, GFE showed a much higher data-efficiency than the autoencoding model, which can be crucial for data scarce applications.