Conditional Diffusion Models

Recent single-stage 3D generative models commonly adopt VecSet representations, encoding 3D shapes as unordered sets of latent tokens. However, compared with two-stage methods that provide explicit positional guidance, these models must implicitly infer token positions throughout denoising, limiting their generation quality. We observe that, despite the absence of explicit positional conditioning, VecSet tokens retain recoverable spatial correspondences. Building on this observation, we propose Position Forcing, a position-based self-conditioning framework. During denoising, Position Forcing recovers token positions from the current clean latent estimate, quantizes them at progressively finer resolutions according to the denoising stage, and feeds the resulting positional encodings back into the diffusion Transformer. This progressively refined positional feedback provides spatial guidance at a granularity appropriate to each denoising stage, guiding shape generation along a coarse-to-fine trajectory and substantially improving generation quality without a separate position generation stage. Experiments demonstrate that Position Forcing achieves strong performance among single-stage 3D generative methods and outperforms several competitive multi-stage approaches.

We revisit a standard accepted practice in the continuous diffusion language model literature of fixing conditioning prompt tokens clean during training. We make a very simple modification: also noise the conditioning prompt tokens during training. We demonstrate that under this modified training objective, we achieve better generalization in combinatorial reasoning tasks such as Sudoku and N-Queens, with the largest gains on harder variants ($3.73\% \to 24.65\%$ solve rate on Sudoku Hard), and increased diversity of generated solutions ($50.60\% \to 73.79\%$ coverage on 10x10 N-Queens). We also show measurable improvements to natural language generation quality in modest dataset regimes with Gigaword summarization, but notably demonstrate that gains do not transfer to all natural language tasks (e.g open ended dialogue generation). Our method is a single line change to the training objective, requires no additional inference costs by default, and provides the flexibility of classifier-free guidance inspired guided sampling. Our code is publicly available.

We study the problem of learning transition kernels for time-homogeneous jump-diffusion processes using conditional diffusion models, with the goal of generating new sample paths from training data consisting of N independent trajectories observed on a high-frequency discrete time grid. On the theoretical side, we establish non-asymptotic bounds for the conditional score estimation error and for the KL divergence between the laws of the true and generated discretely observed paths. On the numerical side, we first evaluate our method on synthetic data to assess the theoretical findings and benchmark its performance against the approach of Gao et al. (2025). We then apply our method to real-world data and investigate its performance on a probabilistic forecasting task.

Accurate and low latency channel estimation is critical for modern MIMO systems, particularly under mobility, where channels exhibit structured sparsity and strong temporal correlation. This paper proposes a time-series conditioned diffusion framework for channel estimation that performs denoising in the angular domain. Starting from least squares (LS) observations, we train a diffusion denoiser whose conditioning information is encoded by a long short-term memory (LSTM) network over a short observation sequence, enabling the model to exploit temporal dynamics beyond per-snapshot estimation. To robustly balance observation fidelity and learned generative priors across a wide signal-to-noise ratio (SNR) range, we introduce a learnable SNR-gated late-fusion shortcut that injects the network input into the final decoding stage through a sigmoid gate with trainable center and scale. To reduce inference latency, we adopt deterministic denoising diffusion implicit model (DDIM) style reverse updates with SNR-adaptive truncation and step allocation, which significantly reduces the number of reverse diffusion steps at high SNR while maintaining strong performance in low SNR regimes. Simulations on time-evolving standardized channel models demonstrate that the proposed method achieves consistent performance gains over existing diffusion-based channel estimation baselines, while retaining low latency through SNR-adaptive inference.

Diffusion models generate data through a continuum of denoising problems, and are widely observed to reveal coarse structure before fine detail. Yet, this intuition is mostly empirical and qualitative. We introduce feature information dynamics, an information-theoretic framework for localizing when a feature is generated during diffusion. Using the I-MMSE identity, we connect the rate of feature mutual information change to a gap between optimal unconditional and feature-conditional denoising losses, yielding practical estimators for feature information density. We further develop a chained decomposition that separates shared from incremental information in a feature hierarchy. We use this framework first to quantitatively confirm spectral autoregression in pixel diffusion, and then to extend the analysis beyond frequency: under a class $\to$ mask $\to$ Canny conditioning chain, the per-feature information densities differ across pixel, SDVAE, VAVAE, and RAE, exposing fundamental differences between these representations and suggesting that ordered generation could be beneficial for training diffusion models. Our code is available at https://github.com/AI4Science-WestlakeU/feature-information-dynamics.

Recent work on language-model adaptation has shown that single models can obtain informative training signals by evaluating their behavior in demonstrationor feedback-augmented contexts, with the help of a teacher network, which is driven by the student's learned parameters. Inspired by this internal-reference principle, we investigate how diffusion models can identify self-referenced training signals without external demonstrations or teacher networks. We introduce SALD, a self-referenced training framework that evaluates each image-caption pair at two noise levels using the same model. The easier, lower-noise path is evaluated without gradient tracking to provide a reference, while the harder, higher-noise path provides the training gradient. Rather than directly distilling the easy-path prediction, SALD uses the difference between two path errors to adapt the hardpath objective. The proposed Advantage-Guided Diffusion (AGD) converts this relative error into a differentiable sample-level weight. Temporal Advantage Memory (TAM) accumulates relative difficulty across training and adapts the future gap between the two noise levels. Spectral Advantage Decomposition (SAD) further compares the residual power spectra of the two paths and constructs a differentiable, frequency-derived latent-element weight. All components share a single set of model parameters, requiring neither an external teacher network nor additional trainable parameters during training or inference, and no modification to the inference procedure. Experiments across multiple architectures and datasets demonstrate consistent improvements in generation quality, while component-wise ablations quantify the contributions of the proposed components.

Foundation models remain vulnerable to spurious correlations and ``Clever Hans'' strategies. Explainable machine learning can find and remove such strategies for classifiers without metadata. For foundation models, no such option exists yet. We propose Disentangled Diffusion Autoencoders (DiDAE). DiDAE wraps a frozen foundation model in a conditional diffusion decoder. A counterfactual is one closed-form edit along a direction of a disentangled dictionary, followed by decoding. The dictionary can be supervised (Procrustes) or unsupervised (Singular Value Decomposition, Sparse Autoencoders). No gradients are needed, so DiDAE is up to 2000 times faster than the state of the art. We evaluate on six datasets, two synthetic and four real-world. In a desiderata-driven benchmark on three of them, its counterfactuals are on par with or better than the state of the art, and they repair downstream classifiers through Counterfactual Knowledge Distillation (CFKD), where they beat metadata-based correction. The same machinery can rank a pretrained dictionary against a trained classifier. It returns the few directions the classifier actually reads, each causally verified by a counterfactual that flips the decision, and repairs the classifier along those a teacher marks spurious. The workflow is plug-and-play in our open-source Peal library we publish alongside the paper. With a public dictionary and a pretrained decoder, all that remains is a cheap linear distillation of the classifier and its own fine-tuning.

This paper proposes MIND, a marginal-invariant neural dependency diffusion model for mixed-type tabular data. MIND does not directly learn the joint distribution in the original heterogeneous feature space. Instead, it first maps different variable types into a unified latent dependency space via column-wise marginal transport. A conditional diffusion model then learns cross-column relationships. Copula-tangent denoising separates known marginal components from learnable dependency residuals. Rank projection during the sampling phase further mitigates marginal shift in reverse diffusion. Experiments across nine diverse tabular benchmarks show that MIND consistently improves marginal fidelity and dependency preservation over existing unified approaches. By explicitly isolating marginal modelling from dependency learning, MIND achieves a strong and stable balance among marginal fidelity, joint dependency preservation, and downstream prediction utility. This work supports separating marginal and dependency modelling as a principled and highly effective paradigm for complex mixed-type tabular generation.

Recent probabilistic weather forecasters train stochastic predictors with the continuous ranked probability score (CRPS) to generate each ensemble member in a single forward pass. These models learn the predictive distribution from the forecast context alone, which becomes difficult at longer forecast horizons where uncertainty is high. To learn the predictive distribution more effectively, we introduce auxiliary conditional denoising tasks that predict the same future state from the context and its corrupted version, which provides partial future information that can reduce prediction ambiguity. Building on distributional diffusion models, we learn the conditional distributions of these tasks with a single stochastic predictor by minimizing a proper scoring rule across noise levels. At inference, the predictor can still generate each ensemble member in a single forward pass at the fully corrupted endpoint. Standard CRPS training is recovered as the endpoint-only special case of our formulation, so our framework extends existing CRPS-based forecasters with only additional conditioning inputs. Controlled experiments show that the auxiliary tasks improve one-step forecasting across architectures, with larger gains at longer forecast horizons. The gains extend to high-dimensional global weather forecasting under both training from scratch and fine-tuning, along with improved calibration and potential benefits for generalization under distribution shift.

Time series imputation has progressed from statistical and deep learning approaches to diffusion-based models, which have shown strong recent performance. Existing diffusion-based methods typically condition the reverse process using local contextual information from the current or neighbouring windows. Meanwhile, global dataset-level structure often remains implicit, limiting performance when local observations are sparse, noisy, or unrepresentative. To address this issue, we propose ProCTI, a diffusion-imputation framework that augments local conditioning with retrieved global dataset-level priors through learned prototypes. A hybrid conditioning mechanism integrates this global context with local signals during reverse diffusion, enabling more accurate reconstruction under varying missingness scenarios. Experiments across multiple benchmark datasets show that ProCTI outperforms strong baselines overall under random missingness, while remaining competitive under attribute-wise missingness. Furthermore, we use a latent-regime data model to characterise the precise conditions under which prototype-derived global conditioning provably improves imputation. We support this with a general theoretical analysis of local-global conditioning.

As the world moves towards sustainable energy sources, hydrogen (H2) can be treated as an eco-friendly alternative to fossil fuels due to its high energy density and zero carbon emissions. The water-gas shift (WGS) reaction is a widely used industrial process for hydrogen production by converting carbon monoxide and steam into hydrogen and carbon dioxide. However, occurrences like severe fouling, catalyst deterioration, and thermal runaway can hamper the reaction kinetics/process safety and decrease the yield of H2. These incidents are rare, and gathering process data under such abnormal conditions is challenging. In this work, we propose a physics-guided conditional diffusion model to generate realistic rare-event trajectories for the WGS reaction. The proposed model integrates a conditional denoising diffusion probabilistic model (CDDPM) with governing laws of the reaction to generate physically consistent process trajectories. The conditioning features allow the model to produce high-quality synthetic profiles for rare-event domains that are typically beyond the training regimes. The generated rare-event trajectories then augment the raw dataset for a balanced distribution between normal and abnormal conditions. We further propose a hazard score to assess the risk severity of the operating condition based on the operating trajectory. Deep learning models are trained with the augmented dataset to diagnose the health status of the reaction. Simulation results show that the proposed physics-guided diffusion model outperforms data-driven models in terms of the quality of synthetic data and diagnosis performance for rare events.

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.

Many physiological time series, such as cardiac and brain recordings, exhibit cyclostationarity: their statistics vary periodically with an underlying cycle phase. Corruption from motion, poor contact, and physiological interference obscures morphology needed for diagnosis, making signal restoration essential. Existing diffusion approaches condition on corrupted observations alone and must learn cyclic structure implicitly. We instead propose two inductive biases which encode cyclostationarity: a shift-covariant wavelet representation and dense per-sample phase conditioning inferred from the corrupted input. We further introduce a training-free cyclostationarity index that quantifies phase structure and predicts when phase conditioning will help. Finally, we propose antithetic coupling of reverse trajectories to reduce sampling variance while achieving comparable performance with fivefold fewer network evaluations. Across modalities, our results show that explicitly encoding measurable cyclic structure improves physiological time-series restoration.

Generating a plausible clinical trajectory does not establish what would happen under a different treatment. We present ADMIT, a framework combining irregular multimodal representations, treatment-conditioned latent diffusion and explicit constraints on generated states or actions. We formulate its interventional target through sequential g-computation and distinguish causal assumptions from constraint satisfaction. Its admissibility mechanism translates physiological prior knowledge into explicit constraints on generated states and proposed actions. Treatment-exposure dynamics condition latent transitions, while state projection or action gating applies the constraints during rollout so that they influence subsequent trajectory generation. In our preliminary experiments, multimodal inputs improved supervised hidden-state recovery and reduced treatment-contrast error. In a simulated dosing-schedule experiment with leak-free history encoding, ADMIT predicted most of the tumor-volume change caused by redistributing a fixed total dose. An exposure input improved these predictions around a temporary dose reduction whether or not the assumed clearance rate was correct, but reduced the predicted size of a dose effect, and a deterministic recurrent baseline matched ADMIT's average predictions. Exposure projection reduced constraint violations, although enforcement remained incomplete. Semi-synthetic experiments using eICU context illustrated treatment-response generation under fixed and adaptive policies. Observational examples further characterize model treatment sensitivity. ADMIT provides a framework for testing whether complementary observations and physiological restrictions improve intervention trajectories, with representation recovery, effect accuracy and rule enforcement assessed separately.

In dyadic human speaker-listener conversations, the listener's facial reactions allows the speaker to accurately perceive the listener's emotional states. Since human facial reactions are non-deterministic, the ability to generate multiple appropriate human-like facial reactions is crucial for realistic human-agent interactions. Although diffusion models are naturally suited to such one-to-many generation, existing diffusion-based Multiple Appropriate Facial Reaction Generation (MAFRG) methods attempt to denoise random Gaussian initialisations directly into multiple appropriate facial reactions (AFRs). These random initialisations are usually not well-aligned with the target listener facial reaction, which requires complex denoising trajectories from these initialisations, and subsequently creates substantial opportunities for deviations away from the range of trajectories leading to appropriate AFRs. Given the inherent mimicry between the human listener's and speaker's facial behaviours, we address the above denoising trajectory issue by leveraging this strong prior. Specifically, we propose ResDiffFRG, a novel diffusion-based MAFRG framework that explicitly anchors the diffusion process to the speaker behaviour by defining its diffusion target as the residual between the speaker anchor and an AFR. The denoiser only needs to model the comparatively small, reaction-specific residual needed to transform this anchor into an AFR, rather than reconstructing the complete reaction from an unstructured state. Extensive experiments show that ResDiffFRG achieves large improvements in correlation-based appropriateness over existing methods. Our denoising trajectory analysis showed that even at the start of the denoising trajectory, ResDiffFRG already achieves a higher facial-reaction correlation score than the Gaussian Diffusion baseline does after completing 60% of its denoising trajectory.

Conditional independence (CI) is a fundamental concept in statistics and machine learning. Recent advances in conditional generative modeling provide flexible tools for generative-model-based CI tests, which rely on an estimated conditional distribution to generate randomized samples. However, errors in estimating this distribution accumulate in existing Type I error bounds, and consistency of the generative estimator alone does not guarantee asymptotic Type I error control. To address this limitation, we formulate conditional generative modeling as a domain adaptation problem and leverage auxiliary data from multiple source domains to improve estimation in the target CI testing domain. We propose Domain-Adapted Diffusion (DA-Diff), a multi-source domain adaptation framework for conditional diffusion models based on weighted empirical risk minimization over both target and source domains. We establish the convergence rate of DA-Diff and show how transferable source data can improve target-domain estimation through an increased effective sample size while controlling transfer bias. Building on DA-Diff, we further propose Domain-Adapted Conditional Independence Testing (DA-CIT) and show that its Type I error satisfies $P(p \leq α) \leq α+ o(1)$. Experiments demonstrate that DA-Diff improved conditional generation quality compared with transfer-learning diffusion baselines, while DA-CIT provides strong Type I error control and competitive power.

Digital zoom transitions between dual cameras often exhibit conspicuous discontinuities in geometric structure and chromatic consistency, degrading the user experience. While recent dual-camera smooth zoom (DCSZ) methods attempt to mitigate this by fine-tuning frame interpolation (FI) models on DCSZ data, they struggle with the large cross-view disparities and complex geometric transformations. Considering that the generative prior of diffusion models is suitable for addressing this problem, we explore their application to DCSZ. However, naively applying existing diffusion-based FI models still yields low-fidelity transitions due to insufficient conditional guidance, high-frequency information loss during VAE encoding, as well as inadequate temporal consistency. To address this, we propose ZoomDiff, a high-fidelity diffusion model that leverages dual-camera inputs in both latent and pixel spaces for photo-realistic transitions. Specifically, we first strengthen dual-image conditional guidance during the multi-step denoising process to improve geometric consistency. Then we inject flow-aligned multi-scale features from the VAE encoder into the VAE decoder to recover high-frequency details, where flow-guided temporal consistency supervision are introduced to produce more smooth transitions. Extensive experiments on both synthetic and real-world datasets demonstrate that ZoomDiff outperforms state-of-the-art methods quantitatively and qualitatively. Project page: https://jiayi-hit.github.io/ZoomDiff.github.io/.

Recent advances in diffusion models highlight the importance of representation regularization for improving sample quality and training efficiency. However, commonly used regularization methods often overlook the built-in conditions (such as labels or texts) which directly determine the generation target. In this work, we demonstrate how conditioning signals affect the feature distribution and introduce the CARE (Condition-Aware REpresentation regularization). CARE is a lightweight plug-and-play regularization framework that dynamically modulates feature distribution based on condition similarity. CARE leverages built-in conditioning signals to judiciously guide the representation space, promoting tighter feature clusters for similar conditions without relying on explicit alignment losses or external supervision. Empirically, CARE consistently improves both visual fidelity and convergence stability across both class-to-image and text-to-image tasks. On ImageNet, CARE achieves a 19.08% reduction in FID in 400k training steps, leading to a 3.5$\times$ speed-up. When applied to text-to-image generation, CARE lowers FID by 16.61% in 200k iterations and improves semantic alignment between generated samples and text prompts. Moreover, CARE can be seamlessly integrated with existing regularization methods, yielding additional performance gains.

Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.

Tracking neurite morphology over time helps characterize structural changes during neuronal development and deterioration, but long-term time-lapse imaging is resource-intensive and difficult to scale. Forecasting future morphology could reduce this burden. Existing neurite digital-twin models such as gated spatiotemporal attention (gSTA) produce a single deterministic forecast without representing variability among plausible futures. We introduce Morphology-Gated Residual Diffusion (MGRD), a compact stochastic surrogate that jointly forecasts twenty future neurite-morphology frames from ten observed frames while conditioning on morphology features derived from the latest observation. On controlled phase-field trajectories, MGRD reduces trajectory-wise mean MAE by 9.7% relative to a matched control while updating 4.46 times fewer parameters. On human iPSC-derived neuron microscopy, MGRD improves all four reported metrics over gSTA, including a 39.6% reduction in trajectory-wise mean MAE and a 45.3% increase in skeleton F1. Without mouse-domain retraining or fine-tuning, MGRD also improves MAE and skeleton F1 on mouse cortical-neurosphere microscopy across 10-40-min sampling intervals and forecast horizons beyond 13 hours. Repeated sampling provides a case-level variance score for ranking forecast difficulty. Retaining approximately 60% of the lowest-variance cases reduces mean MAE by 17.6% on iPSC microscopy and 16.8% on simulation data. MGRD uses 1.01% of gSTA's parameters, requires less than one tenth of its training-update time, and generates a 50-step DDIM trajectory 7.9% faster when morphology features are cached. These results establish MGRD as a compact stochastic surrogate for neurite-morphology forecasting and case prioritization across simulation and microscopy datasets.

Diffusion models are increasingly adapted from generation to conditional prediction, where a conditioning signal is combined with an evolving noisy representation of the target. In fully supervised segmentation, however, the conditioning image can already support direct target prediction, so endpoint performance alone establishes neither reliance on the added diffusion state nor a deterministic advantage over image-only prediction. For state reliance, we disrupt target-derived state content or correct image-state pairing during retraining of twelve published methods across three datasets, with ten matched seeds per setting. All 40 original-method comparisons whose evaluated-mask routes remained downstream of noised-quantity reconstruction exhibited state reliance, whereas all 30 comparisons with a segmentation-supervised bypass preserved reference performance. Rerouting five originally bypass-capable methods by forcing segmentation supervision through noise-to-mask reconstruction converted all 30 corresponding comparisons from preserved performance to state reliance. For deterministic utility, matched image-only counterparts achieved similar or better performance in 28 of 35 settings overall, including 16 of 20 whose native methods relied on both audited state properties. These results identify supervision path as a determinant of state reliance in the audited methods. Separately, matched image-only counterparts show that diffusion-specific computation often provides no deterministic endpoint advantage, including in methods that rely on the audited state properties. More generally, when conditioning already supports strong target prediction, diffusion-specific claims require additional evidence that the added state is used and that diffusion-specific computation improves the claimed capability beyond a matched condition-only counterpart.

Forecasting anatomical changes such as tumor growth and neurodegeneration is a challenging generative vision task. Morphological evolution is subtle relative to static anatomy, highly patient-specific, and inherently stochastic. Existing methods struggle with several issues: deterministic networks ignore biological stochasticity, while standard diffusion models require computationally prohibitive multi-pass sampling to quantify uncertainty. We propose MUMINS (Metadata-conditioned Uncertainty-aware Medical Image Next-state Synthesis), an efficient diffusion framework that jointly diffuses a baseline scan and its follow-up residual, summed to synthesize the follow-up scan, while concurrently predicting a spatial uncertainty map, in a single reverse diffusion process. Conditioned on the time interval and relevant metadata, it preserves fine-grained anatomy by dynamically re-injecting the baseline as a soft anchor at every denoising step, and a negative-log-likelihood head learns the uncertainty map to explicitly flag error-prone regions. Designed without organ-specific heuristics, the same architecture is reused across anatomies via separate, dataset-specific retraining. Extensive evaluations demonstrate that dataset-specific retraining of MUMINS matches or outperforms dedicated, domain-specific state-of-the-art methods on lung CT (PNG) and brain MRI (OASIS-3). Project page: https://github.com/aolivtous/MUMINS.

Facial Landmark Detection(FLD) is a crucial task in various applications and has achieved significant advancements in recent years. However, current FLD methods still struggle under challenging conditions, where facial structural variations, information loss, and noise interference severely compromise the integrity and accuracy of learned facial features. To address these issues, we propose Frequency-Adaptive Heatmap-Conditional Diffusion Network (FAHCD-Net), which integrates a Frequency-Adaptive Heatmap-Conditional Diffusion (FAHCD) model with a Smoothness Regularization (SR) loss in a cascaded framework. Specifically, the FAHCD model incorporates a Hierarchical Frequency Adaptation (HFA) module designed to suppress redundant high-frequency noise through multi-layer frequency decomposition and adaptive reconstruction, thereby preserving essential facial structures. Additionally, the SR loss is proposed to further mitigate the interference of high-frequency noise and enhance the smoothness of the generated landmark heatmaps. By cascading the FAHCD model with the SR loss, FAHCD-Net effectively leverages both statistical and frequency-based distribution characteristics of the data to progressively generate more accurate landmark heatmaps from noisy inputs. Extensive experiments on popular benchmarks demonstrate the effectiveness and robustness of the proposed method, achieving state-of-the-art performance in FLD tasks under challenging scenarios. The source code is available at https://github.com/HJWKryptonite/FAHCD-Net.

The energy transition is reshaping residential electricity consumption through the increasing adoption of distributed generation, electrified appliances, and demand-response programs. Understanding these evolving behaviors requires access to granular smart-meter data for applications such as load forecasting, appliance detection, and demand-side flexibility analysis. However, such data are subject to strict access restrictions and data-protection regulations. Thus, realistic synthetic alternatives are necessary. In this paper, we introduce LoaDiff, a diffusion-based generative model for year-long, sub-hourly smart-meter load curves. LoaDiff supports flexible conditioning on static household attributes, such as appliance ownership, and dynamic contextual variables, including calendar information and outdoor temperature. We evaluate the model against multiple generative baselines on three residential electricity-consumption datasets. Our experiments assess four complementary dimensions: fidelity and diversity, training-record memorization risk, downstream utility for load forecasting and appliance detection, and conditional controllability under alternative temperature conditions. The results show that LoaDiff generates realistic and diverse load profiles, achieves a favorable trade-off between generation quality and limited evidence of memorization, preserves information useful for downstream energy applications, and responds coherently to changes in conditioning variables.

Multivariate time series imputation (MTSI) aims to recover missing values in temporal data composed of multiple interdependent variables. This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems. Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising. However, most existing approaches perform diffusion directly in the original data space, requiring the denoising network to simultaneously capture global structure, temporal dynamics, and stochastic variability. This makes the generative task unnecessarily complex, especially when modern deterministic imputers can already provide accurate initial reconstructions. To address this limitation, we propose RDDMPI, a conditional residual diffusion framework that operates directly in residual space. Instead of modeling the full missing signal directly, we reformulate probabilistic imputation as a baseline-residual decomposition, where a pretrained model captures the dominant signal and a diffusion process models the residual uncertainty. To better exploit deterministic guidance, \model{} conditions the reverse denoising process on both the baseline-completed signal and its latent representation, while a reliability-aware conditioning mechanism adaptively controls the influence of baseline information during residual generation. This formulation simplifies the diffusion learning objective, enabling it to focus on structured correction terms rather than reconstructing the full signal. Experiments on multiple benchmark datasets demonstrate that RDDMPI consistently improves both reconstruction accuracy and uncertainty quantification.

Current conditioned generative models heavily rely on score functions for guidance during training. When the generative model is a diffusion process with a singular diffusion coefficient and the underlying (conditional) densities either do not exist or are not smooth, we use causal optimal transport to define \emph{approximate} loss functions that identify a minimum-entropy control for guidance under minimal assumptions. Our approach relies on causal optimal transport and its characterization through the predictable representation property of (conditioned) diffusion processes whose associated martingale problem is well posed, à la Üstünel.

Predicting storm surge induced by landfalling tropical cyclones is crucial for flood mitigation and coastal risk management. Traditionally, physics-based numerical models simulate storm surge by solving the Navier--Stokes equations using numerical methods, but these simulations are computationally expensive. Generative models are promising for storm surge emulation because they can generate diverse realizations rather than producing a single deterministic prediction. However, their use for storm surge emulation remains largely unexplored. In this paper, we leverage diffusion models for storm surge surrogate modeling, combining a baseline prediction stage with conditional generation to provide a more interpretable modeling framework. We develop SurgeGen, a two-stage generative framework for generating storm surge scenarios conditioned on hypothetical storms with parameters defined in a continuous space. First, a baseline model produces a coarse estimate of the storm surge height. This estimate then conditions a diffusion model, which generates refined storm surge scenarios that better capture spatial patterns and variability. We demonstrate that our approach can generate realistic and diverse storm surge scenarios under conditions both within and outside the training distribution.

Diffusion models have recently emerged as expressive generative priors for planning and control. This paper studies Action Diffusion, an action-sequence diffusion formulation used as an open-loop proposal distribution for a point-mass system with dry friction and stiction. In this benchmark, motion starts only when the applied input exceeds a static-friction threshold, so effective controls occupy a small and temporally structured subset of the action-sequence space. A compact conditional 1D U-Net generates bounded control sequences conditioned on initial and target states. We compare it with uniform random shooting, random shooting from the same structured dataset prior, and the Cross-Entropy Method (CEM). Results show that Action Diffusion reduces terminal error and stuck steps, especially in low-sample regimes. These results indicate that conditional diffusion provides an effective mechanism for generating temporally coherent control sequences that overcome stiction by conditioning and recombining structured control primitives from the training prior for state-to-state open-loop control.

Localized extreme precipitation is a major trigger of urban flash floods and landslides, yet producing nowcasts that combine fine spatial detail with probabilistic uncertainty remains challenging. Here we introduce exPreCast-ENS, a conditional residual diffusion framework that transforms the deterministic 4 km radar nowcaster exPreCast into a 1 km probabilistic ensemble while correcting systematic forecast errors. Conditioning on both the forecast and preceding radar observations lets the ensemble-mean correct the baseline rather than perturb it, while members represent unresolved fine-scale variability. Over the Korean Peninsula, skill improves with ensemble size. In two high-impact events in 2023, a 30-member ensemble recovers 38-47% of heavy-rain pixels missed by exPreCast while retaining approximately 95% of its correct detections and alarming on under 1% of the pixels it correctly left clear. The method generates a 1-h forecast in 3.4 s on a single GPU and yields consistent improvements on the French regional MeteoNet radar dataset.

Subseasonal-to-seasonal (S2S) precipitation forecasting has substantial financial and societal impact, yet remains challenging because of weak predictive signals, high associated uncertainty, and the computational cost of operational systems, which constrains simulation fidelity. We introduce SimCast-S2S, a generative latent-diffusion framework for probabilistic S2S precipitation forecasting that addresses three major bottlenecks in data-driven prediction. First, because S2S prediction requires uncertainty quantification rather than only deterministic point forecasts, SimCast-S2S is the first data-driven system that uses a diffusion-based generative pipeline for S2S prediction, enabling effective sampling from the underlying conditional distribution. Second, since generating large probabilistic ensembles is computationally costly in physical space, SimCast-S2S instead operates in a compact latent space learned by variational autoencoders (VAEs), enabling efficient large-ensemble generation. Third, diffusion models typically require large training datasets; SimCast-S2S overcomes this via transfer learning with low-rank adaptation (LoRA), pretraining on large ensembles of climate simulations before fine-tuning on limited reanalysis data. On reanalysis data, SimCast-S2S outperforms deep learning baselines, including convolutional neural networks and U-Net architectures. Notably, despite using only a subset of atmospheric input variables and no post-processing, bias correction, or calibration, SimCast-S2S remains competitive with, and in many aspects outperforms, state-of-the-art operational systems such as the ECMWF-S2S baseline. These results indicate that latent generative modeling combined with simulation-to-reanalysis transfer learning offers an efficient and scalable path toward data-driven probabilistic S2S precipitation forecasting.