Diffusion Dynamics

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.

Data is important in many deep learning-based inverse problem solvers. However, obtaining sufficient paired data in many scenarios remains highly challenging, while unpaired data is cheap. To maximize data utilization, this paper proposes LUD-DIF, a diffusion-based approach for solving inverse problems with unpaired data. Starting from the evidence lower bound (ELBO) of the joint distribution, we decouple it into two independent diffusion processes under the weak-coupling assumption. The method provides theoretical support from a variational inference perspective, derives the loss function, quantitatively analyzes the error bound introduced by the assumption, and offers a theorem-motivated heuristic for hyperparameter selection. Experimental results demonstrate that LUD-DIF achieves outstanding performance on multiple image inverse problems, validating its effectiveness and generalization capability in unpaired inverse problem settings.

3D brain MRI generation has made significant advances in medical imaging, simulation, and controllable anatomical analysis. However, existing generative models typically synthesize 3D volumes monolithically, often overlooking regional anatomical structures and limiting local controllability. To address these limitations, we introduce AnaDiffusion, an anatomically compositional latent diffusion framework that factorizes the generation process into distinct, anatomically meaningful regions, followed by part-to-whole assembly and global refinement. Our approach first trains part diffusion models to capture local structural priors. We then inject an assembled anatomical composite of the parts into the whole-brain latent representation and continue denoising. This mechanism enables the model to resolve global context while preserving the injected anatomy. As a result, AnaDiffusion produces both explicit part assets and a globally coherent volume, thereby enabling controllable part editing without requiring subject-specific dense segmentation maps at inference time while maintaining consistent part-to-whole brain structure. On the subject-disjoint ADNI test split, AnaDiffusion achieves the lowest FID across the whole brain, left and right hemispheres, cerebellar-brainstem complex, and seam regions. It also achieves the best cerebellar and second-best ventricular and brainstem absolute Cohen's d values among the evaluated methods. In localized editing experiments, paired MS-SSIM demonstrates high target transfer and off-target preservation, supporting controllable part replacement with minimal unintended anatomical alterations.

Quantitative MRI (qMRI) provides standardised tissue parameter maps, but the reliability of deep learning-based qMRI mapping methods is often not explicitly characterised. In this work we systematically evaluate uncertainty maps for quantitative MRI derived from multiple inferences of a data-consistent diffusion model-based qMRI framework. Evaluation on synthetic test data assessed error-awareness, high-error detection, selective prediction, and Gaussian interval calibration. Diffusion model-derived uncertainty was positively associated with the mapping error, while risk-coverage analysis showed that excluding high-uncertainty voxels reduced the retained error. However, the raw uncertainty was poorly calibrated for quantitative interval interpretation. Calibration was substantially improved using a post-hoc procedure combining prediction-value-dependent bias correction with scalar uncertainty scaling. Qualitative evaluation on a healthy volunteer showed spatially meaningful uncertainty patterns. These results indicate that diffusion model-derived uncertainty is informative for reliability assessment and selective prediction, but requires calibration for quantitative interval interpretation.

The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires jointly modeling discrete crystallographic symmetry, elemental composition, and continuous geometry. We introduce DynaCrys, a generative model for crystals in which the space group co-evolves with Wyckoff occupations and elements through a coupled symbolic diffusion process. The structured space-group transitions follow crystallographic group-subgroup relations. As the space group changes, a shared, pretrained symmetry codebook provides both the legality-constrained stochastic decoder and the symmetry-constrained crystal-geometry model with a common representation of the corresponding Wyckoff vocabulary. Across large-scale evaluations using two independent relaxation-and-evaluation engines, DynaCrys achieves best-in-class performance in symmetry-aware discovery of stable, unique, and novel crystals, both overall and under the additional requirement of nontrivial post-relaxation symmetry. It also enables fast sampling while generating structures with consistently low relaxation-induced structural displacements.

3D human registration has historically been treated as a regression task, assuming a unique ground-truth alignment exists between the template and an input point cloud. In reality, acquisition noise, occlusions, and unknown soft tissue dynamics introduce inherent ambiguity into human scans. Regression-based methods consequently converge to an average prediction, often failing to represent a plausible geometry. In our work, we embrace such uncertainty by modeling the registration as a distribution of alignments. We propose ODin, which formulates registration as a 3D diffusion process that generates a point cloud aligned with the target geometry while preserving template semantics through consistent point ordering. To achieve this, ODin relies on global, local, and positional conditioning, guiding each point to its correct location. Our experiments demonstrate that such a generative formulation not only outperforms its regression-based baseline, but also establishes a new state of the art, surpassing highly engineered methods while reducing the registration time by two-thirds. Pre-trained models and code are available at https://riccardomarin.github.io/odin/.

Machine olfaction for gas unmixing is an underconstrained inverse problem in which gas compositions must be inferred from low-dimensional, delayed, and entangled sensor responses produced by interacting chemical transport, surface adsorption, and sensor transduction. One of the key obstacles is physics closure misspecification, where a neural network is designed to fit sensor traces rather than infer a physically closed olfactory process. In this work, we formulate gas unmixing as a multi-physics-constrained inverse problem governed by Maxwell--Stefan multicomponent transport PDEs, competitive adsorption ODEs, and nonlinear sensor transduction ODEs. Directly solving such a high-dimensional coupled system is computationally expensive and often numerically unstable. To this end, we propose UnMixNet, a physics-closed graph neural solver that embeds this multi-physics forward process into end-to-end gas unmixing. UnMixNet discretizes Maxwell--Stefan cross-diffusion on spatial graphs and formulates the multicomponent flux on each edge. This design enables local, differentiable, and flux-conservative inference for multicomponent cross-diffusion. Evaluations on SmellNet show improved single-odor recognition, seen-mixture unmixing, and unseen-mixture generalization. In addition, an external validation on UCI Dynamic Gas Mixtures shows that the inferred concentration process agrees with ground truth concentration set points under dynamic transitions. Process-consistency diagnostics further show that the proposed model learns transferable dynamic physical fingerprints that better satisfies transport, conservation, adsorption, and readout closure.

Supercharging of lithium-ion batteries (LiBs) requires robust health monitoring to ensure durability, safety, and user confidence, particularly for emerging vehicle-to-grid applications with bidirectional energy flows. Yet battery management remains largely disconnected from the material and structural origins of aging, limiting both interpretable health assessment and informed battery design. Here we propose a physics-informed learning framework with virtual sensing that infers hard-to-measure design parameters, including solid-state diffusion coefficient, electrode thickness, ion concentration, and particle size, directly from standard battery management system (BMS) measurements. Across diverse fast-charging strategies and driving profiles, embedding a digital-twin-derived particle-cracking mechanism as a soft constraint reduces trajectory and lifetime prediction errors by 6-8 times relative to state-of-the-art machine learning baselines using only 2% early-life observations. We further show that accurate degradation extrapolation does not require fully resolved governing equations; validated partial mechanisms, jointly refined with limited data, provide sufficient guidance. Virtual sensing transforms standard charging signals into latent design variables without additional sensors, bridging observable battery behavior and underlying aging processes while reducing capacity loss error by up to 39%, end-of-life (EOL) error by 17%, and prediction variability by up to 54%, enabling real-time exploration of new battery configurations. More broadly, the proposed framework establishes a practical feedback loop between deployment and development, demonstrating how real-world operation can continuously inform upstream design decisions across complex multiphysics systems.

Diffusion-weighted imaging (DWI) is acquired as part of bi-parametric prostate MRI, but suffers from artifacts that degrade downstream quantitative and diagnostic performance. While DWI preprocessing is standard in brain imaging, its adoption in prostate imaging remains limited and lacks standardized pipelines. This study investigated the effect of different DWI preprocessing strategies on apparent diffusion coefficient (ADC) estimation and automatic Prostate Imaging Reporting and Data System (PI-RADS) classification. 268 cases were derived from the fastMRI prostate cohort by sequentially applying denoising, Gibbs-ringing correction, and diffeomorphic registration for susceptibility distortion correction. ADC maps were compared using linear least squares (LLS) and iteratively-weighted LLS (IWLLS). A 3-class DenseNet classifier was trained to predict PI-RADS scores from multi-channel MRI inputs. ADC analysis revealed statistically significant differences across preprocessing pipelines, with LLS and IWLLS producing numerically equivalent maps. Linear relationships between ADC values were preserved across most datasets (PCC ~0.99), while distortion correction realigned DWI to T2w anatomy and altered ADC values accordingly (PCC ~0.90). Classification showed the best AUROC and sensitivity for high-risk PI-RADS classes in the fully processed dataset. False-negative analysis revealed this dataset produced the least overconfident incorrect predictions on high-risk classes, which is a desirable property for clinical triage. DWI preprocessing, particularly distortion correction, enhances both ADC map quality and the predictive power of deep learning models for PI-RADS classification, supporting the need for optimized preprocessing pipelines in prostate MRI.

AI models are increasingly trained on personal images scraped from social media and public platforms, often without consent, leading to serious privacy violations, such as unauthorized facial recognition and targeted advertising. To counter this, researchers have developed unlearnable examples (UEs), images modified with imperceptible noise to prevent AI models from extracting meaningful information. However, existing UE methods primarily rely on pixel-space noise, which can be bypassed by relearning strategies such as adversarial training, image transformation, and compression. While some techniques improve robustness, they often come at the expense of significant degradation in image utility and perceptual quality. In this paper, we introduce DiffUE to overcome these limitations by injecting noise into the semantic space of images instead of the pixel space. Instead of corrupting pixel values, DiffUE modifies high-level semantic features of images, ensuring robust unlearnability while preserving visual quality and utility. By leveraging a diffusion-based autoencoder framework to manipulate semantic features, DiffUE generates purposeful, natural-looking modifications that effectively resist advanced relearning strategies. Extensive experiments on four datasets, CIFAR-10, CIFAR-100, CelebA-HQ, and ImageNet, as well as a subjective user study, demonstrate that DiffUE significantly enhances the trade-off between image quality and unlearnability, offering a more robust and effective solution for safeguarding personal data in an increasingly exploitative AI landscape.

Diffusion models are increasingly utilized for modeling molecular structures and conformational ensembles, yet the thermodynamic meaning of their learned representations and scores remains elusive. To resolve this ambiguity, we introduce a mathematically consistent action-operator framework natively compatible with diffusion models. By defining a fixed molecular environment as a base action $S_0(x)$ and an alchemical perturbation as an operator $O(x)$, standard diffusion noising induces effective noised actions and operators whose gradients and alchemical derivatives are directly represented by the model's learned fields. This rigorous self-consistency enables a ``noisy operator bridge'' capable of reading out free-energy differences ($ΔF$) from endpoint ensembles and per-frame evaluations. In controlled experiments on alanine dipeptide systems, we show that incorporating physical inductive biases enables partial recovery of the base action and perturbation operator. When applied to a challenging C6-H to C6-F ligand-pocket nonbonded perturbation (185L/IND) with negligible phase-space overlap, our supervised bridge estimates the alchemical $ΔF$ within approximately $1\ k_\mathrm{B}T$ of a stable 19-state MBAR reference. Finally, we demonstrate that endpoint coordinates and binary labels alone are sufficient to partially recover the operator shape and a centered free-energy scale without any force or action supervision. This work provides a rigorous path toward transforming generative molecular diffusion models from black-box coordinate samplers into auditable thermodynamic estimators.

Sampling from an unnormalized target density by reversing an Ornstein-Uhlenbeck diffusion requires the score of each noise-perturbed marginal law. Two exact identities are available: Tweedie's identity and a target-score identity, each yielding unbiased finite-reference score estimators for the OU-marginal score. Score estimators induced by scalar blends of Tweedie and TSI score estimators can reduce variance, but they are too rigid for singular or strongly anisotropic targets. We formulate blended score estimation as a conditional risk-minimization problem over matrix valued blending coefficients, referred to as gates. Our central result is to show the optimal matrix valued gate for blended score estimation is given $$G_\star(y,t) = α_t^2 \left(α_t^2 I_d + γ_t\, \mathbb{E}[H_0(X_0)\mid Y_t=y] \right)^{-1}, \qquad H_0=-\nabla^2\log p_0 .$$ Here $α_t = e^{-t}$ and $γ_t = 1-e^{-2t}$ are the OU coefficients, and the conditional expectation is under the OU posterior of $X_0$ given $Y_t=y$. We call this formula the \emph{Laplace-Fisher Gate Identity} (\LFGI{}). Because the Tweedie-TSI disagreement has conditional mean zero, the gate changes the score-estimator variance but not its expected value. We derive the variance-optimal matrix gate, record the Gaussian special case, and establish finite-reference consistency and stability bounds for estimating the gate from weighted reference samples. We then use the finite-reference LFGI score estimator for normalized density evaluation in Bayesian inverse problems. In regimes where MCMC pilot samples and derivative information are already available, LFGI uses those byproducts to construct a normalized surrogate for the posterior density. The resulting surrogate supplies information that the MCMC samples alone do not provide: posterior-energy evaluation, model-evidence estimation, and downstream density-based diagnostics. On a PDE-constrained inverse-problem benchmark, the LFGI surrogate improves posterior-density calibration and sampling diagnostics relative to the other tested score-estimator classes. Experiments using LFGI with known model evidence check absolute evidence calibration in both Gaussian and non-Gaussian settings.

Diffusion models are typically sampled independently, even when the downstream objective is to obtain a diverse set of candidates. We introduce a variance-weighted batch distribution that favours collections of samples with large empirical spread after a prescribed linear feature map. The target is specified explicitly, and the sampler is derived as the corresponding Doob $h$-transform of independent diffusion dynamics. The resulting correction has a compact form: an interaction term that repels posterior denoised means, together with a curvature term that moves particles to the region of higher feature variance. This yields an interacting-particle sampler with a transparent probabilistic target rather than a heuristic repulsive drift.

While longitudinal brain PET imaging is the gold standard for quantifying the spatiotemporal accumulation of Beta-amyloid, its widespread clinical utility is constrained by high operational costs and cumulative radiation risks. Recent deep generative models show promise in longitudinal image synthesis; however, they often fail to capture subtle pathological progression due to identity drift and a persistent bias toward trivially replicating baseline signal intensities rather than modeling temporal transition. To this end, we propose Delta-Diffusion, a novel progression-aware framework that redefines longitudinal PET synthesis as a conditional Poisson Diffusion Bridge (PDB) process. Unlike standard diffusion models that start from Gaussian noise, our PDB formulation is mathematically anchored to the subject's baseline PET, effectively transforming the generative task into a conditional distribution transition of the amyloid trajectory. To handle heteroscedastic nature of PET imaging, we introduce a physically-grounded Poisson perturbation within a Diffusion Transformer (DiT). This architecture uses adaptive scale-shift modulation to precisely calibrate the synthesis with the elapsed clinical interval and structural MRI context. A volume-of-interest balanced objective is designed to emphasize sparse, high-risk regions of amyloid accumulation. Validated on two cohorts with 542 subjects, Delta-Diffusion demonstrates superior performance in capturing longitudinal variations in amyloid deposition compared to state-of-the-art methods, offering a robust computational framework for tracking disease progression.

Inversion-based image editing offers flexible and training-free control but still struggles with inversion accuracy and the trade-off between editing fidelity and background preservation. While recent methods improve inversion formulations or attention interactions, the role of textual conditioning in shaping diffusion dynamics and editing behavior remains underexplored. We show both empirically and theoretically that the precision of textual conditioning influences inversion stability by modulating the geometry of the diffusion velocity field, while also affecting the consistency of cross-branch attention during editing. These effects directly impact background preservation and semantic fidelity. Building on this analysis, we propose SimEdit, a conditioning-aware framework with two complementary components: (a) conditioning refinement, which constructs conditioning signals with improved semantic precision and structural alignment to facilitate stable inversion and consistent attention manipulation, and (b) token-wise cross-branch attention control, which separates edit-relevant and structure-preserving components and modulates them asymmetrically during attention manipulation. Extensive experiments on PIE-Bench demonstrate that SimEdit consistently improves both inversion reconstruction quality and editing performance over previous attention-manipulation approaches. Our code is available at https://github.com/zju-pi/SimEdit.

Diffusion models have seen wide adoption for 3D molecular generation, yet they offer no principled signal of when a generated molecule is likely to be of low quality. We propose a post-hoc method for estimating per-sample uncertainty in pretrained molecular diffusion models. Building on a Laplace approximation of the denoising network, we measure the variability of the noise prediction across the generation trajectory. Empirically, we show that the resulting uncertainty score is informative of sample quality, exhibiting a negative correlation with established sample-level quality metrics. We further study how the proposed uncertainty score can be used to filter generated samples, improving model performance via test-time scaling.

Latent diffusion models leverage visual tokenizers to compress images into latent spaces for efficient generative modeling. However, better reconstruction quality of a tokenizer does not necessarily translate into better generation quality, suggesting that latent representations should be evaluated not only by fidelity but also by their diffusability. Recent studies have proposed diverse explanations for diffusion-friendly latent spaces, including semantic separability, affine equivariance, distribution uniformity, spatial structure, spectral smoothness, and manifold continuity. Yet these properties are often validated on a limited set of tokenizers, leaving it unclear which factors are most predictive of downstream generation quality and whether such conclusions hold beyond the specific settings in which they are introduced. In this work, we conduct a systematic study of latent diffusability by training a large collection of tokenizers with diverse regularization strategies, architectures, and latent configurations, and evaluating them with multiple downstream diffusion backbones. Our analysis identifies several latent properties that consistently correlate with generation quality and exhibit strong generalization across experimental settings. Beyond existing metrics, we introduce Velocity Irreducible Variance (VIV), a measure of velocity ambiguity induced by trajectory crossings. Extensive experiments show that VIV is one of the most stable predictors of generation quality.

Image customization learns target subjects from reference concept images and generates conditioned images per text prompts, mainly modifying styles or backgrounds. Prevailing methods adopt fine-tuning to pack diverse concept attributes into a unified latent embedding, yet entangled attributes hinder elimination of irrelevant disturbances from style and background. To address this issue, we propose Equilibrated Diffusion, a frequency-driven approach that disentangles tangled concept features for balanced customization and consistent text-visual matching. Unlike conventional methods learning full concepts with shared embeddings and unified tuning, our work utilizes the inherent link between image frequency components and semantics: low frequencies represent subject content and high frequencies correspond to styles. We decompose concepts in frequency space and optimize each embedding independently. This separate optimization enables the denoiser to capture style detached from subject identity and generalize better to unseen stylistic prompts. Merging multi-frequency embeddings preserves the model's original spatial customization ability. We further deploy mask-guided diffusion to restrict irrelevant background changes and boost text alignment. Residual Reference Attention (RRA) is inserted into spatial attention to retain subject structure and identity consistency. Experiments prove Equilibrated Diffusion exceeds mainstream baselines on subject fidelity and text adherence, verifying our method's superiority.

Diffusion models have emerged as a leading framework for deep generative modeling. While the standard Gaussian formulation is theoretically convenient, its suitability for heavy-tailed datasets remains unclear. To address this, heavy-tailed diffusion models (HTDMs) extend the standard formulation by replacing the Gaussian distribution with a Student's t-distribution, thereby improving tail fidelity on heavy-tailed datasets. Although stochastic differential equation (SDE)-based sampling is possible in HTDMs, it has not been fully explored. In this paper, we propose an SDE-based sampler for HTDMs that explicitly incorporates a state-dependent diffusion coefficient. This state dependence naturally induces a self-regulating annealing mechanism by adaptively modulating the effective noise scale. We theoretically explore this mechanism and experimentally verify its necessity for reproducing samples from a heavy-tailed distribution.

Bayesian inference provides a principled framework for modeling epistemic uncertainty in neural networks by treating predictions as distributions rather than deterministic values. Meanwhile, diffusion-based models for 3D molecular graph generation operate on fragile geometric structures governed by strict chemical constraints, making inference highly sensitive to uncertainty miscalibration. A largely overlooked issue is that epistemic uncertainty arising from the learned denoiser interacts with the aleatoric uncertainty intentionally injected during reverse diffusion, leading to systematic variance inflation and a mismatch between the true distribution and the simulated distribution. This effect is particularly detrimental for high-precision molecular generation, where even small deviations can violate chemical validity. In this work, we provide a theoretical and empirical analysis of how epistemic uncertainty propagates through diffusion inference and degrades sampling quality. Building on this investigation, we propose UCD (Uncertainty-Calibrated Diffusion), a simple yet effective method that calibrates the reverse diffusion process to account for epistemic uncertainty. Extensive experiments on standard 3D molecular benchmarks demonstrate that UCD consistently improves sampling quality across diverse baseline methods, establishing new state-of-the-art performance for 3D molecular diffusion. The code is available at https://github.com/jiuguaiwf/UCD.

Aspect-Based Sentiment Analysis (ABSA) encompasses seven distinct subtasks, each focusing on different extracted elements. Despite the proven success of generative models in unified aspect sentiment analysis, existing approaches often rely on auto-regressive token-by-token generation without grasping the whole information of the aspect and opinion terms, resulting in boundary insensitivity, particularly in context of multi-word aspect and opinion terms. To address these issues, we present DiffuSent, a non-auto-regressive diffusion framework that systematically formulates all ABSA subtasks as boundary denoising diffusion processes, progressively refining boundaries over noisy states. Furthermore, we introduce a contrastive denoising training strategy which effectively address duplicate predictions with subtle variations introduced by diffusion process. Extensive experiments across 28 settings (7 subtasks x 4 datasets) demonstrate that DiffuSent achieves delivers consistent improvements over the strongest generative and span-based systems. DiffuSent exhibits notable gains on multi-word triplets, achieving an average improvement of +2.48 F1, and maintains robust extraction accuracy in sentences containing multiple sentiment triplets. Moreover, the non-auto-regressive decoding enables substantial efficiency benefits, reaching up to 181 times faster inference than auto-regressive generative baselines

Synthesizing high fidelity contrast enhanced MRI is clinically valuable for safer and more efficient breast cancer screening, yet remains challenging due to complex lesion textures and heterogeneous enhancement patterns.

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models.

Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with heterogeneous materials with extreme stiffness contrasts, hyperelasticity under large deformations, and contact-rich interactions, which are common scenarios in the real world. We present DiffPhD, a unified GPU-accelerated differentiable Projective Dynamics framework for heterogeneous materials that tackles these intertwined challenges simultaneously. Our key insight is a careful integration of: (i) stiffness-aware projective weights to embed heterogeneity into the global system; (ii) trust-region eigenvalue filtering lifted to the backward pass for stable hyperelastic gradients and a type-II Anderson Acceleration scheme with dual-gate convergence to stabilize forward iteration under large stiffness contrasts; and (iii) a unified GPU pipeline that reuses a single sparse factor across forward, backward, and contact computations, with stiffness-amplified Rayleigh damping folded into the same factor for heterogeneity-aware dissipation at zero recurring cost. DiffPhD achieves strict gradient accuracy while delivering up to an order-of-magnitude speedup over prior differentiable solvers on heterogeneous, hyperelastic, contact-rich benchmarks. Crucially, this speedup does not come at the cost of stability: DiffPhD remains convergent on stiffness contrasts up to 100x where prior PD solvers degrade. This unlocks end-to-end gradient-based optimization on regimes previously bottlenecked by either solver fragility or per-iteration cost -- shell--joint composite creatures, soft characters wielding stiff weapons, and soft-gripper robotic manipulation -- all handled within a single forward--backward pass.

When reliable target structures are unavailable at scale or phenotypes arise from dysregulated pathways, transcriptomic perturbations provide a system-level functional readout for drug action. In this work, we formalize \emph{Transcriptome-based Drug Design (TBDD)} as a generative inverse problem: designing drug molecules conditioned on desired transcriptomic state transitions. We analyze the inherently ill-posed nature of this task, which is further complicated by the profound domain gap between biology and chemistry and by the sparsity of transcriptomic signals. To address these challenges, we propose \textbf{\themodel{}} (A \textbf{C}ell\textbf{U}lar \textbf{R}esponse \textbf{E}ngine), a multi-resolution transcriptome-guided diffusion framework. \themodel{} features a specialized \textbf{Transcriptome Perturbation Functional Feature Extractor (TFE)} that (1) distills function-oriented perturbation embeddings from pre/post states, (2) aligns these signatures to dual chemical views to bridge the cross-modal gap, and (3) performs heterogeneity-aware aggregation to extract robust state-specific signals from noisy transcriptomic data. Extensive evaluations on both standard benchmarks and rigorous out-of-distribution protocols demonstrate that \themodel{} consistently outperforms strong baselines in structural quality and functional consistency. Furthermore, we validate its practical utility via a zero-shot gene-inhibitor design task, highlighting the potential of phenotype-driven generative discovery.

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce temporal variability in the reverse dynamics. We reinterpret PS from a dynamical perspective, showing that the standard PS update corresponds to a first-order discretization of the diffusion dynamics plus a residual correction capturing the mismatch between the denoised prediction and the data-consistent estimate. A second-order discretization, however, naturally introduces a temporal correction based on the variation of consecutive estimates. Building on this, we propose LAMP, combining the second-order update with the residual correction characterizing a PS technique. LAMP thus inherits a lagged temporal correction, and it can be implemented as a modular plug-in over the PS backbone. We show that LAMP preserves the structure of a posterior sampler, and we perform a one-step risk analysis to characterize when LAMP improves the reverse transition via a bias-variance trade-off. Experiments across multiple imaging tasks demonstrate consistent improvements over strong baselines such as DiffPIR and DDRM, without increasing the number of denoising evaluations.

Imitation learning powered by generative models has proven effective for modeling complex single-agent behaviors. However, teaching multi-agent systems, like multiple arms or vehicles, to coordinate through imitation learning is hindered by a fundamental data bottleneck: as the joint state-action space grows exponentially with the number of agents, collecting a sufficient amount of coordinated multi-agent demonstrations becomes extremely costly. In this work, we ask: how can we leverage single-agent demonstration data to learn multi-agent policies? We present Coordinated Diffusion (CoDi), a framework that couples independently trained single-agent diffusion policies through a user-defined multi-agent cost function, without requiring any coordinated demonstrations. We derive a new diffusion-based sampling scheme wherein the diffusion score function decomposes into independent, single-agent pre-trained base policies plus a cost-driven guidance term that coordinates these base policies into cohesive multi-agent behavior. We show that this guidance term can be estimated in a gradient-free manner, making CoDi applicable to black-box, non-differentiable cost functions without additional training. Theoretically and empirically, we analyze the conditions under which this composition can faithfully approximate a target multi-agent behavior. We find a complementary role for demonstration data versus the cost function: single-agent demonstrations must cover the support of the desired multi-agent behavior, while the cost function must promote desired behavior from this product of single-agent policies. Our results in simulation and hardware experiments of a two-arm manipulation task show that CoDi discovers robust coordinated behavior from single-agent data, is more data-efficient than multi-agent baselines, and highlights the importance of joint guidance, base policy support, and cost design.

3D asset generation plays a pivotal role in fields such as gaming and virtual reality, enabling the rapid synthesis of high-fidelity 3D objects from a single or multiple images. Building on this capability, enabling style-controllable generation naturally emerges as an important and desirable direction. However, existing approaches typically rely on style images that lie within or are similar to the training distribution of 3D generation models. When presented with out-of-distribution (OOD) styles, their performance degrades significantly or even fails. To address this limitation, we introduce \textbf{DiLAST}: 2D Diffusion-based Latent Awakening for 3D Style Transfer. Specifically, we leverage a pretrained 2D diffusion model as a teacher to provide rich and generalizable style priors. By aligning rendered views with the target style under diffusion-based guidance, our method optimizes the structured 3D latent representations for stylization. We observe that this limitation stems not from insufficient model capacity, but from the underutilization of structured 3D latents, which are inherently expressive. Despite being trained on comparatively limited data, 3D generation models can leverage 2D diffusion guidance to steer denoising toward specific directions in latent space, thereby producing diverse, OOD styles. Extensive experiments across diverse data and multiple 3D generation backbones demonstrate the effectiveness and plug-and-play nature of our approach.

The lack of analytical models describing diffusion time dependence at intermediate time scales in complex tissue microstructure limits the accurate quantification of extracellular diffusivity and tissue microstructure. We introduce TRACED, a biophysical model that incorporates diffusion time dependence in cell distributions to quantify pathologically-relevant properties in solid tumors. Neural networks were trained on Monte Carlo diffusion simulations using sphere distribution-based geometries to enable the rapid computation of time-dependent diffusion MRI signals in cell populations of variable cell size. Model sensitivity and fit performance were assessed via simulation. Diffusion data from eight mixed-grade glioma patients was fitted using the TRACED model. Data fitting was performed using a novel physics-informed transfer learning pipeline, Sim2PINN. In two patients, cell size measurements were compared directly with image-localized histology. Simulation results indicate improved parameter estimation compared to the simple two-compartment model. TRACED enabled the simultaneous in vivo quantification of intracellular volume fraction, cell size distribution, extracellular intrinsic diffusivity, and tortuosity in glioma patients. Neural network implementations of diffusion time-dependence and tortuosity showed behavior consistent with coarse-graining and effective medium theory, respectively. Future work will explore the clinical utility of TRACED parameters in additional patients.

Using reinforcement learning, we optimize for practical hardware constraints, including limited FIR filter taps at the transmitter and receiver, mean photon number and finite DAC/ADC resolution. Under these realistic conditions, the proposed approach achieves significant performance improvements.

Synthesizing longitudinal medical images at controllable disease stages while preserving patient-specific anatomy is hindered by the entanglement of pathological textures and structural features. We address this challenge for ulcerative colitis (UC) endoscopy, where severity follows a continuous ordinal progression along the Mayo Endoscopic Score (MES). Our framework, Disentangled Anatomy-Disease Diffusion (DADD), conditions a latent diffusion model on two complementary embeddings: a pretrained image encoder for patient anatomy and a separately trained ordinal embedder for cumulative disease severity. Since image embeddings inevitably capture disease information, we introduce a Feature Purifier, a cross-attention-based erasure mechanism that identifies and suppresses disease-correlated channels, yielding purified anatomical representations. These cleaned anatomy tokens and target disease tokens are injected into the denoising network via a Triple-Pathway Cross-Attention mechanism with resolution-dependent routing gates. This architecture leverages the U-Net hierarchy, in which different network depths encode global structure versus fine-grained pathological texture. Furthermore, we introduce Delta Steering, a training-free directional signal derived from the ordinal embeddings that enables explicit, single-pass control over disease transitions at inference without requiring additional forward passes. Validated on the LIMUC dataset, our approach produces high-fidelity images across all severity levels and effectively rebalances skewed class distributions, enhancing performance for downstream classification tasks. The dataset is available at zenodo.org/records/5827695 and the code base at github.com/umutdundar99/progressive-stable-diffusion

Segmentation models such as Segment Anything Model (SAM) and SAM2 achieve strong prompt-driven zero-shot performance. However, their training on natural images limits domain transfer to medical data. Consequently, accurate segmentation typically requires extensive fine-tuning and expert-designed prompts. We propose DiffuSAM, a diffusion-based adaptation of SAM2 for prompt-free medical image segmentation. Our framework synthesizes SAM2-compatible segmentation mask-like embeddings via a lightweight diffusion-prior from off-the-shelf frozen SAM2 image features. The generated embeddings are integrated into SAM2's mask decoder to produce accurate segmentations, thereby eliminating the need for user prompts. The diffusion prior is further conditioned on previously segmented slices, enforcing spatial consistency across volumes. Evaluated on the BTCV and CHAOS datasets for CT and MRI under Source-Free Unsupervised Domain Adaptation (SF-UDA) and Few-Shot settings, DiffuSAM achieves competitive performance with efficient training and inference. Code is available upon request from the corresponding author.

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time trajectory increments, state-space partitioning, or repeated simulation of candidate models, which become unreliable or computationally expensive for high-dimensional systems, coarse temporal sampling, or unevenly sampled data. We introduce a data-driven calibration method based on a novel relationship between the coefficients of a stochastic reduced model and the conditional score of the finite-time transition density, defined as the gradient of the logarithm of the transition density with respect to the initial state. The resulting identity expresses derivatives of lagged correlation functions as stationary expectations over observed lagged pairs involving this conditional score and the unknown model coefficients. This formulation allows the drift and diffusion structure to be constrained directly from finite-lag statistics, without differentiating trajectories, partitioning state space, or repeatedly integrating candidate reduced models during calibration, yielding a least-squares fitting problem over stationary lagged pairs. We validate the approach on three systems of increasing complexity: an analytically tractable Cox--Ingersoll--Ross diffusion, a two-dimensional nonequilibrium diffusion with affine multiplicative noise, and a periodic soft-spin stochastic Landau--Lifshitz chain. Across these tests, the inferred models preserve the invariant statistics while reproducing finite-lag dynamical correlations. The framework provides a scalable route for learning stochastic reduced-order models from data that reproduce prescribed statistical and dynamical properties.

This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, we propose a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. We also prove that our filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edge-preserving process. Under the conditions established for the diffusivity and using a stopping criterion for the diffusion time, we get piecewise constant images with a low computational effort. Finally, we test our filter with real images and we illustrate the effects of our diffusivity function as a method to get piecewise constant images. The code is available at https://github.com/cplatero/NonlinearDiffusion.

We present LLaDA2.0-Uni, a unified discrete diffusion large language model (dLLM) that supports multimodal understanding and generation within a natively integrated framework. Its architecture combines a fully semantic discrete tokenizer, a MoE-based dLLM backbone, and a diffusion decoder. By discretizing continuous visual inputs via SigLIP-VQ, the model enables block-level masked diffusion for both text and vision inputs within the backbone, while the decoder reconstructs visual tokens into high-fidelity images. Inference efficiency is enhanced beyond parallel decoding through prefix-aware optimizations in the backbone and few-step distillation in the decoder. Supported by carefully curated large-scale data and a tailored multi-stage training pipeline, LLaDA2.0-Uni matches specialized VLMs in multimodal understanding while delivering strong performance in image generation and editing. Its native support for interleaved generation and reasoning establishes a promising and scalable paradigm for next-generation unified foundation models. Codes and models are available at https://github.com/inclusionAI/LLaDA2.0-Uni.

Diffusion models have emerged as powerful tools for a wide range of vision tasks, including text-guided image generation and editing. In this work, we explore their potential for object grounding in remote sensing imagery. We propose a hybrid pipeline that integrates diffusion-based localization cues with state-of-the-art segmentation models such as RemoteSAM and SAM3 to obtain more accurate bounding boxes. By leveraging the complementary strengths of generative diffusion models and foundational segmentation models, our approach enables robust and adaptive object localization across complex scenes. Experiments demonstrate that our pipeline significantly improves localization performance, achieving over a 14% increase in Acc@0.5 compared to existing state-of-the-art methods.

Reconstructing 3D human motion and human-object interactions (HOI) from Internet videos is a fundamental step toward building large-scale datasets of human behavior. Existing methods struggle to recover globally consistent 3D motion under dynamic cameras, especially for motion types underrepresented in current motion-capture datasets, and face additional difficulty recovering coherent human-object interactions in 3D. We introduce a two-stage framework leveraging 2D diffusion that reconstructs 3D human motion and HOI from Internet videos. In the first stage, we synthesize multi-view 2D motion data for each domain, leveraging 2D keypoints extracted from Internet videos to incorporate human motions that rarely appear in existing MoCap datasets. In the second stage, a camera-conditioned multi-view 2D motion diffusion model is trained on the domain-specific synthetic data to recover 3D human motion and 3D HOI in the world space. We demonstrate the effectiveness of our method on Internet videos featuring challenging motions such as gymnastics, as well as in-the-wild HOI videos, and show that it outperforms prior work in producing realistic human motion and human-object interaction.

In this paper, we consider the problem of extraction of most informative features from time series that are regarded as observed values of stochastic processes satisfying the It{ô} stochastic differential equations with unknown random drift and diffusion coefficients. We do not attract any additional information and use only the information contained in the time series as it is. Therefore, as additional features, we use the parameters of statistically adjusted mixture-type models of the observed regularities of the behavior of the time series. Several algorithms of construction of these parameters are discussed. These algorithms are based on statistical reconstruction of the coefficients which, in turn, is based on statistical separation of normal mixtures. We obtain two types of parameters by the techniques of the uniform and non-uniform statistical reconstruction of the coefficients of the underlying It{ô} process. The reconstructed coefficients obtained by uniform techniques do not depend on the current value of the process, while the non-uniform techniques reconstruct the coefficients with the account of their dependence on the value of the process. Actually, the non-uniform techniques used in this paper represent a stochastic analog of the Taylor expansion for the time series. The efficiency of the obtained additional features is compared by using them in the autoregressive algorithms of prediction of time series. In order to obtain pure conclusion that is not affected by unwanted factors, say, related to a special choice of the architecture of the neural network prediction methods, we used only simple autoregressive algorithms. We show that the use of additional statistical features improves the prediction.

Sampling based on score diffusions has led to striking empirical results, and has attracted considerable attention from various research communities. It depends on availability of (approximate) Stein score functions for various levels of additive noise. We show how in some generality, the availability of scores allows the general problem to be ``reduced'' to sampling from an adaptively constructed sequence of $K$ strongly log-concave (SLC) sub-problems. The reduction is simple, constructive and algorithm-independent, so that any SLC sampler can be used as a subroutine. Various bounds on score-based sampling complexity follow directly: for instance, high-accuracy SLC samplers yield $\tilde{\mathcal{O}}(K \sqrt{d} \operatorname{polylog}(1/\varepsilon))$ guarantees for accuracy $\varepsilon$ in dimension $d$, where randomized midpoint SLC schemes yield $\tilde{\mathcal{O}}(K d^{1/3} \operatorname{poly}(1/\varepsilon))$ guarantees. When the original distribution itself is SLC, we prove that $K \leq 1 + \log_2(κ)$, thereby obtaining the first efficient procedure with logarithmic dependence on condition number $κ$; for general distributions, the quantity $K$ depends on the geometry of score Hessian across the trajectory. Our analysis is direct and simple, involving techniques and insights complementary to those in standard analyses of discretized diffusions.

Recent progress in text-to-video generation has achieved remarkable realism, yet fine-grained control over camera motion and orientation remains elusive, especially with extreme trajectories (e.g., a 180-degree turnaround, or looking directly up or down). Existing approaches typically encode camera trajectories using relative or ambiguous representations, limiting precise geometric control and offering limited support for large rotations. We introduce GimbalDiffusion, a framework that enables camera control grounded in physical-world coordinates, using gravity as a global reference. Instead of describing motion relative to previous frames, our method defines camera trajectories in an absolute coordinate system, allowing accurate, interpretable control over camera parameters. Using panoramic 360-degree videos for training, we cover the full sphere of possible viewpoints, including combinations of extreme pitch and roll that are out-of-distribution of conventional video data. To improve camera control, we introduce null-pitch conditioning, a strategy that prevents the model from overriding camera specifications in the presence of conflicting prompt content (e.g., generating grass while the camera points toward the sky). Finally, we propose new benchmarks to evaluate gravity-aware camera-controlled video generation, assessing models' ability to generate extreme camera angles and quantify their input prompt entanglement.

Data unlearning aims to remove the influence of specific training samples from a trained model. In fine-tuning methods, data unlearning relies primarily on loss maximization over forget samples, which often leads to quality degradation or incomplete forgetting. Existing methods perform unlearning uniformly across diffusion stages, ignoring diffusion dynamics from noise to data. Our systematic study of diffusion phases shows that forgetting in diffusion models is uneven across time and frequency, with theoretical justification of distributive distortion and forgetting-utility trade-off. By selectively forgetting time and frequency in diffusion models, we achieve both higher unlearning success rates and improved generation quality across diverse settings, including both conditional and unconditional scenarios. We also introduce an improved SSCD metric that measures dissimilarity using a normalized perturbation distance. Together, we provide practical insights for understanding and improving data unlearning in diffusion models.

Urban sensor networks need forecasts that are accurate, carry useful uncertainty, and refresh fast enough to act on as new readings arrive. These goals conflict: deterministic models give no distribution, while diffusion forecasters model uncertainty but denoise from pure noise over many steps. We present Double-Diffusion, which integrates a closed-form graph-heat prior into a denoising diffusion model. The prior is a parameter-free low-pass forecast over the sensor graph, and it serves two roles: it is the residual target the model generates, and it conditions the denoiser. The reverse process therefore starts near the prior and denoises a short warm-started chain instead of synthesizing from pure noise; the name denotes this composition, a graph diffusion feeding a denoising diffusion. A compact denoiser, DD-Net, is trained as a Denoising Diffusion Probabilistic Model (DDPM) in the Resfusion warm-start formulation, so generation refines the prior over a short truncated chain rather than synthesizing from pure noise; a graph-spectral read-out of the prior residual sets its switchable spatial filter per domain from training data alone. On four real-world air quality and traffic networks, Double-Diffusion attains the best CRPS of all probabilistic methods on every dataset and stays competitive in point accuracy with the strongest baselines, at a fraction of the sampling cost of from-noise diffusion. The code is available at: https://github.com/teddyicare/Double-Diffusion

The substantial training cost of diffusion models hinders their deployment. Immiscible Diffusion recently showed that reducing diffusion trajectory mixing in the noise space via linear assignment accelerates training by simplifying denoising. To extend immiscible diffusion beyond the inefficient linear assignment under high batch sizes and high dimensions, we refine this concept to a broader miscibility reduction at any layer and by any implementation. Specifically, we empirically demonstrate the bijective nature of the denoising process with respect to immiscible diffusion, ensuring its preservation of generative diversity. Moreover, we provide thorough analysis and show step-by-step how immiscibility eases denoising and improves efficiency. Extending beyond linear assignment, we propose a family of implementations including K-nearest neighbor (KNN) noise selection and image scaling to reduce miscibility, achieving up to >4x faster training across diverse models and tasks including unconditional/conditional generation, image editing, and robotics planning. Furthermore, our analysis of immiscibility offers a novel perspective on how optimal transport (OT) enhances diffusion training. By identifying trajectory miscibility as a fundamental bottleneck, we believe this work establishes a potentially new direction for future research into high-efficiency diffusion training. The code is available at https://github.com/yhli123/Immiscible-Diffusion.