conditional diffusion forecasting

This work addresses the challenge of zero-shot conditional generation from pretrained unconditional diffusion models—specifically, generating samples satisfying complex logical constraints (e.g., structural conditions on tables, images, or time series) without fine-tuning. We propose a neural-symbolic soft-constraint embedding method that encodes first-order logic constraints as differentiable soft penalties and directly perturbs the score function to achieve theoretically consistent approximation of the conditional distribution—bypassing classifier-guided sampling or costly retraining. Our approach integrates score-based modeling, symbolic logic encoding, score correction, and stabilized sampling. Experiments across diverse data modalities demonstrate that our method achieves high-fidelity approximation of the true conditional distribution, significantly outperforming existing zero-shot conditional generation baselines.

This work addresses the fundamental trade-off between discrete-time modeling and continuous-time stochastic differential equation (SDE) modeling in denoising diffusion probabilistic models (DDPMs) and score-based generative models (SGMs). Specifically, it tackles the challenge that discretization-induced errors propagate through reverse sampling, degrading sample quality. To this end, we first unify discrete and continuous modeling paradigms by deriving a total variation (TV) distance bound—integrating discrete Girsanov transformation, Pinsker’s inequality, and the data processing inequality. This bound rigorously characterizes the performance limits of both frameworks. We further obtain an analytically tractable TV upper bound that quantitatively exposes the coupled influence of step size, noise schedule, and score estimation error. Our theoretical results provide principled, information-theoretic guidance for designing efficient and robust discrete-time sampling algorithms in diffusion models.

This work addresses the challenge of conditional sampling in generative diffusion models for Bayesian inverse problems. It systematically surveys and unifies two dominant paradigms: end-to-end methods based on the joint distribution, and decoupled approaches combining a pre-trained marginal distribution with an explicit likelihood model. We propose, for the first time, a theoretically consistent unified framework that integrates Monte Carlo sampling, diffusion process reweighting, conditional probability construction, and fine-tuning techniques—rigorously characterizing the underlying assumptions and intrinsic relationships among these methods. The framework bridges theoretical gaps across disparate conditional generation strategies and delivers a scalable, interpretable, and theoretically grounded toolkit for conditional sampling in scientific computing inverse problems, including image reconstruction and physics-based simulation.

Efficient conditional sampling from high-dimensional, multimodal posterior distributions remains challenging in uncertainty quantification. Method: We propose a non-iterative, non-invertible generative modeling framework. Leveraging the analytically tractable conditional score function under a Gaussian mixture prior, we construct a training-free diffusion model; a feedforward neural network directly predicts the denoising direction, bypassing invertibility constraints of normalizing flows and iterative solvers of conventional diffusion models. Sampling is achieved via a single forward pass using backward ordinary differential equation (ODE) integration and noise-label supervision. Contribution/Results: Experiments demonstrate that our method achieves state-of-the-art accuracy while significantly accelerating sampling—by multiple times over existing approaches—making it particularly suitable for real-world uncertainty quantification tasks such as parameter estimation in complex physical systems.

This work addresses weak interpolation controllability and training instability in conditional generation. We propose Conditional Stochastic Interpolation (CSI), a framework that enables differentiable and controllable transport from a reference distribution to a target conditional distribution by modeling conditional probability flows or stochastic differential equations (SDEs). Key contributions include: (i) the first explicit formulation of the conditional drift and score function as conditional expectations; (ii) an adaptive diffusion term that enhances training stability; (iii) a non-asymptotic error bound guaranteeing convergence and generalization; and (iv) support for parameter-free regression estimation, deterministic ODE sampling, and adaptive-diffusion sampling. Extensive experiments on standard image datasets demonstrate high-quality, high-fidelity conditional generation. The method combines theoretical rigor—grounded in conditional probability flow theory—with practical effectiveness, offering improved controllability, stability, and flexibility over existing approaches.

This study systematically investigates the parameter inference capability of diffusion models in simulation-based inference (SBI), targeting fast, high-precision estimation of latent parameters and flexible modeling of conditional or joint distributions between parameters and observations. We propose a novel paradigm integrating guidance mechanisms, fractional composition, flow matching, consistency modeling, and joint modeling. For the first time, we rigorously characterize the coupled impact of noise scheduling, parameterization, and sampling strategies on both statistical accuracy and computational efficiency. We establish a comprehensive, end-to-end practical framework—spanning model design, training, inference, and evaluation—and validate its robustness and generalizability across multidimensional benchmarks varying in parameter dimensionality, simulation budget, and simulator architecture. Our work provides both theoretical foundations and an actionable implementation framework for trustworthy deployment of diffusion models in SBI.

This work identifies a systematic “non-denoising” behavior in practical sampling of conditional diffusion models: under text or observational conditioning, their denoising trajectories consistently deviate from the theoretically ideal path, causing inconsistent generation across algorithms such as DDPM and DDIM. To quantify this phenomenon, the authors introduce *Schedule Deviation*, a novel metric that—through empirical analysis and theoretical justification—demonstrates for the first time that this deviation stems from an inherent inductive bias, independent of model capacity or dataset scale. Further, via theoretical analysis and manifold consistency verification, they establish that smoothness priors fundamentally impede alignment across conditional denoising flows. This work provides an interpretable diagnostic tool for conditional diffusion models and advances the development of robust conditional sampling strategies and training paradigms.

This work addresses the challenge of data assimilation in nonlinear, non-Gaussian systems under model-agnostic (black-box) conditions by proposing a closed-form conditional diffusion model that requires no neural network training. The method constructs a joint distribution of states and observations via kernel density estimation and derives an analytical expression for the conditional score function, enabling efficient sampling and state estimation. As the first framework to integrate closed-form score functions with diffusion models for data assimilation, it eliminates the reliance of traditional filters on Gaussian assumptions and explicit dynamical models. Experiments on the Lorenz-63 and Lorenz-96 systems demonstrate superior performance over ensemble Kalman filters and particle filters, even with small to moderate ensemble sizes.

This work addresses the lack of a systematic theoretical understanding of how finite-sample learning, neural network parameterization, and numerical discretization jointly affect generation quality in diffusion models. The authors develop a unified framework for convergence and generalization analysis, decomposing the overall generation error— for the first time—into four interpretable components: forward truncation error, backward discretization error, generalization error (accounting for both data finiteness and forward discretization), and optimization gap. Leveraging a ResNet-type score estimator and combining tools from numerical analysis of stochastic differential equations with total variation distance bounds, they quantitatively characterize the joint influence of training sample size, temporal grid density, and optimization accuracy on generation fidelity, thereby establishing end-to-end theoretical guarantees.