The paper proposes a new approach to likelihood approximation for complex simulation models using a chain of aggregated normalizing flows. It describes a sequential estimation strategy where each set of bijective transformations is optimized independently, enabling scalable and controllable simulation routines for large‑scale data analysis. The framework also offers a surrogate model that facilitates sample generation, Bayesian inference, hypothesis testing, and uncertainty quantification.
arXiv:2606. 30489v1 Announce Type: cross Abstract: Normalizing Flows excel at modeling a single fixed density, yet many problems across the sciences, such as high energy physics, instead require modeling how that density deforms as a function of continuous parameters: the strength of a physical effect, a calibration constant, or a source of systematic uncertainty.
The paper introduces Normalizing Flow Maps (NFM), a new class of exactly invertible pushforward maps that extend normalizing flows and flow maps by learning the integrator of an underlying dynamical system while enabling efficient exact likelihood evaluation. NFMs incorporate two consistency axes—pointwise matching for β1-based regression losses and distributional matching for aligning pushforward distributions with a forward process—allowing scalable training. Experiments on CIFAR-10, ImageNet-64, and Boltzmann Generators demonstrate that NFMs achieve state‑of‑the‑art sample quality among parameter‑matched normalizing flows and outperform prior normalizing flows on peptide benchmarks.
arXiv:2504. 01894v2 Announce Type: replace Abstract: We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution.
The paper introduces Transformed Samplers with Variance Reduction, a method that extends exact control variate solutions from simple reference densities to general target distributions by learning a bijective change of variables, such as a normalizing flow. By training the flow to map the target close to the reference in latent space, the authors show that Markov kernels and their Poisson solutions transform accordingly, enabling explicit control variates in the latent space. The resulting estimator is consistent under mild tail conditions, and the approach also applies to importance sampling, with experiments demonstrating competitive performance against state‑of‑the‑art samplers and control variates.
The paper introduces NeVI‑Cut, a modular variational inference method for cut‑Bayes that does not require access to upstream data or models. It approximates the cut‑posterior by minimizing the expected downstream conditional Kullback‑Leibler divergence, using conditional normalizing flows as the variational family. The authors provide fixed‑data convergence rates, establish uniform KL approximation results for flow classes, and demonstrate the algorithm’s speed and accuracy on several applications.
arXiv:2607. 03809v1 Announce Type: new Abstract: Normalising flows provide a powerful variational family for approximate inference, yet individual architectures often fail to generalise across heterogeneous posterior geometries.
The paper introduces ENFR, a method for estimating the absolute evidence ζ of a data‑generating model in Bayesian inference. It learns Bayes factors relative to a flow‑matched reference and then recovers the absolute evidence, improving over existing flow‑based baselines across multiple applications. The authors also provide a joint architecture for estimating evidences of multiple models and demonstrate its performance and scalability on diverse scientific datasets.
Conditional Mean Flows introduce a new approach for simulation-based inference that replaces the costly numerical integration of traditional flow matching with few-step sampling and tractable density evaluation. By identifying conditional flow maps through a mean flow objective and using independent masking, the method allows direct estimation of marginal likelihoods. Experiments demonstrate that single-step conditional mean flow density evaluation achieves error comparable to 200-step flow matching while accelerating downstream MCMC sampling by roughly 200‑fold.
arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
arXiv:2512. 04954v3 Announce Type: replace Abstract: We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling.
The paper introduces a new approach to source distribution estimation (SDE) in simulation-based science, addressing limitations of existing methods that rely on a fixed surrogate likelihood. By employing an expectation‑maximization framework, the authors iteratively train an amortized posterior on fresh simulations (E‑step) and refit the source distribution to the posterior’s average (M‑step). Two parameterizations are explored: separate source and posterior flows, and a single shared conditional flow, with experiments on three benchmark tasks showing improved performance over fixed surrogate and iterated baseline methods, notably achieving higher data‑space C2ST scores on the Lotka–Volterra benchmark.
arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.