Kornelius Raeth 1 Nicole Ludwig 1 2 Abstractscoring rules distribute the training gradient in proportion to Sample-based generative models are increasingly data density, with no awareness of the decision maker's cost structure. The model's limited capacity is allocated globused for probabilistic forecasting in high-stakes ally, leaving decision-critical regions of the output space decision settings, yet their training objectives are potentially underserved. These models are commonly trained with strictly proper Given a forecast, a decision maker with cost function c(a,y), scoring rules, such as the energy score, which al-of action aand outcome y, selects the action that minimises locate their training signal in proportion to dataexpected cost under the forecast distribution; a point forecast density, with no awareness of where forecast eris insufficient to evaluate this expectation. A good forecast rors are most costly for downstream decisions. Crucially, the energy score objective with a differentiable deci-observed cost of the optimal action is itself a proper scoring sion loss that directly penalises the cost incurredrule (Hartline et al., 2025; Kleinberg et al., 2023), placing by acting on the model's forecast. This combinedit in the same family as the energy score which licenses loss is theoretically grounded, as the decision losstheir combination as a theoretically well-founded training is itself a proper scoring rule. Introduction score acts as that anchor, preventing the model from collapsing outside cost-sensitive regions. Our method is theo-tion based on a temperature forecast, balancing asset loss against the cost of intervention. In the weather domain, retically grounded and leads to better downstream decisions state-of-the-art forecasting systems (Lang et al., 2024; Pricewhile retaining full probabilistic forecasts, as validated on et al., 2023) are trained with strictly proper scoring rulessynthetic and real-world forecasting tasks. A gradient analysis showing which regions benefitscore reduces to the continuous ranked probability score from the decision loss and why, based on the cost (CRPS), widely used in meteorological forecast verificafunction structure. Both model classes introduced above are commonly trained by minimising strictly proper sion calibration.

We introduce a framework for Thompson sampling (TS) contextual bandit algorithms, in which the algorithm's ability to quantify uncertainty and make decisions depends on the quality of a generative model that is learned offline. Instead of viewing uncertainty in the environment as arising from unobservable latent parameters, our algorithm treats uncertainty as stemming from missing, but potentially observable outcomes (including both future and counterfactual outcomes). If these outcomes were all observed, one could simply make decisions using an oracle policy fit on the complete dataset. Inspired by this conceptualization, at each decision-time, our algorithm uses a generative model to probabilistically impute missing outcomes, fits a policy using the imputed complete dataset, and uses that policy to select the next action. We formally show that this algorithm is a generative formulation of TS and establish a state-of-the-art regret bound. Notably, our regret bound depends on the generative model only through the quality of its offline prediction loss, and applies to any method of fitting the oracle policy.

How should we evaluate the quality of generative models? Many existing metrics focus on a model's producibility, i.e. the quality and breadth of outputs it can generate. However, the actual value from using a generative model stems not just from what it can produce but whether a user with a specific goal can produce an output that satisfies that goal. We refer to this property as steerability. In this paper, we first introduce a mathematical decomposition for quantifying steerability independently from producibility.

Adapting large-scale foundational flow and diffusion generative models to optimize task-specific objectives while preserving prior information is crucial for real-world applications such as molecular design, protein docking, and creative image generation. Existing principled fine-tuning methods aim to maximize the expected reward of generated samples, while retaining knowledge from the pre-trained model via KL-divergence regularization. In this work, we tackle the significantly more general problem of optimizing general utilities beyond average rewards, including risk-averse and novelty-seeking reward maximization, diversity measures for exploration, and experiment design objectives among others. Likewise, we consider more general ways to preserve prior information beyond KL-divergence, such as optimal transport distances and Rényi divergences. To this end, we introduce Flow Density Control (FDC), a simple algorithm that reduces this complex problem to a specific sequence of simpler fine-tuning tasks, each solvable via scalable established methods. We derive convergence guarantees for the proposed scheme under realistic assumptions by leveraging recent understanding of mirror flows. Finally, we validate our method on illustrative settings, text-to-image, and molecular design tasks, showing that it can steer pre-trained generative models to optimize objectives and solve practically relevant tasks beyond the reach of current fine-tuning schemes.

We introduce PARTCRAFTER, the first structured 3D generative model that jointly synthesizes multiple semantically meaningful and geometrically distinct 3D meshes from a single RGB image. Unlike existing methods that either produce monolithic 3D shapes or follow two-stage pipelines, i.e. first segmenting an image and then reconstructing each segment, PARTCRAFTER adopts a unified, compositional generation architecture that does not rely on pre-segmented inputs.

We consider inferring the causal effect of a treatment (intervention) on an outcome of interest in situations where there is potentially an unobserved confounder influencing both the treatment and the outcome. This is achievable by assuming access to two separate sets of control (proxy) measurements associated with treatment and outcomes, which are used to estimate treatment effects through a function termed the causal bridge (CB). We present a new theoretical perspective, associated assumptions for when estimating treatment effects with the CB is feasible, and a bound on the average error of the treatment effect when the CB assumptions are violated. From this new perspective, we then demonstrate how coupling the CB with an autoencoder architecture allows for the sharing of statistical strength between observed quantities (proxies, treatment, and outcomes), thus improving the quality of the CB estimates. Experiments on synthetic and real-world data demonstrate the effectiveness of the proposed approach relative to state-of-the-art methodology for causal inference with proxy measurements.

A curious phenomenon observed in some dynamical generative models is the following: despite learning errors in the score function or the drift vector field, the generated samples appear to shift along the support of the data distribution but not away from it. In this work, we investigate this phenomenon of robustness of the support by taking a dynamical systems approach on the generating stochastic/deterministic process. Our perturbation analysis of the probability flow reveals that infinitesimal learning errors cause the predicted density to be different from the target density only on the data manifold for a wide class of generative models. Further, what is the dynamical mechanism that leads to the robustness of the support? We show that the alignment of the top Lyapunov vectors (most sensitive infinitesimal perturbation directions) with the tangent spaces along the boundary of the data manifold leads to robustness and prove a sufficient condition on the dynamics of the generating process to achieve this alignment. Moreover, the alignment condition is efficient to compute and, in practice, for robust generative models, automatically leads to accurate estimates of the tangent bundle of the data manifold. Using a finite-time linear perturbation analysis on samples paths as well as probability flows, our work complements and extends existing works on obtaining theoretical guarantees for generative models from a stochastic analysis, statistical learning and uncertainty quantification points of view. Our results apply across different dynamical generative models, such as conditional flow-matching and score-based generative models, and for different target distributions that may or may not satisfy the manifold hypothesis.

Recent advances in generative modeling have shown significant promise in designing novel periodic crystal structures. Existing approaches typically rely on either large language models (LLMs) or equivariant denoising models, each with complementary strengths: LLMs excel at handling discrete atomic types but often struggle with continuous features such as atomic positions and lattice parameters, while denoising models are effective at modeling continuous variables but encounter difficulties in generating accurate atomic compositions. To bridge this gap, we propose CrysLLMGen, a hybrid framework that integrates an LLM with a diffusion model to leverage their complementary strengths for crystal material generation. During sampling, CrysLLMGen first employs a fine-tuned LLM to produce an intermediate representation of atom types, atomic coordinates, and lattice structure. While retaining the predicted atom types, it passes the atomic coordinates and lattice structure to a pre-trained equivariant diffusion model for refinement. Our framework outperforms state-of-the-art generative models across several benchmark tasks and datasets. Specifically, CrysLLMGen not only achieves a balanced performance in terms of structural and compositional validity but also generates more stable and novel materials compared to LLM-based and denoisingbased models Furthermore, CrysLLMGen exhibits strong conditional generation capabilities, effectively producing materials that satisfy user-defined constraints.

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Effectively leveraging prior knowledge of a system's physics is crucial for applications of machine learning to scientific domains. Previous approaches mostly focused on incorporating physical insights at the architectural level. In this paper, we propose a framework to leverage physical information directly into the loss function for prediction and generative modeling tasks on systems like molecules and spins. We derive energy loss functions assuming that each data sample is in thermal equilibrium with respect to an approximate energy landscape. By using the reverse KL divergence with a Boltzmann distribution around the data, we obtain the loss as an energy difference between the data and the model predictions.