生成模型理论与方法

Recent motion generative models have demonstrated strong capabilities in synthesizing physically plausible character motion, but often overlook established animation principles used by professional animators to ground and design their animation work. Understanding and incorporating these principles into motion generative pipelines is essential for producing motions that serve not only physically grounded applications but also the needs of the character animation community. This enables the creation of characters that not only move in physically plausible ways but also feel alive, expressive, and engaging. To close this gap, we focus on the Exaggeration principle of animation and investigate how it can be incorporated into modern motion generative pipelines to produce more expressive character motions. To this end, we introduce a framework that operates at two stages of existing motion generative pipelines. The first stage introduces exaggeration during training, where we perform supervised fine-tuning of pre-trained text-to-motion models on our curated exaggeration dataset. The second stage operates at inference time, where we: (i) introduce a mathematical formulation of exaggeration based on dynamic movement primitives (DMPs); and (ii) leverage this formulation as an exaggeration guidance signal to guide existing diffusion and flow-matching text-to-motion generation models toward exaggerated motion without additional training. Through qualitative and quantitative evaluations against three strong motion generation models, we show that our methods generate more exaggerated and expressive motions while preserving neutral reference motion intent and physical plausibility.

RNA function arises from the coupling of nucleotide sequence and three-dimensional structure, motivating their joint design. Coordinating global folding with nucleotide-level detail remains challenging under limited structural supervision. We introduce La-Ribo, a generative framework for RNA sequence-structure co-design via geometry-latent flow matching. La-Ribo retains a sparse phosphate-sugar--base scaffold and encodes nucleotide identity and local conformation in residue-wise latents. A shared flow network generates both jointly, and an RNA-specific decoder then reconstructs all heavy atoms. To expand supervision, we construct a quality-controlled corpus of 168,561 RNA structures, integrating experimental data with predictions from three folding models, including 10,631 MSA-supported structures generated in this work. La-Ribo improves designability and codesignability over the evaluated baselines across sampling budgets and two refolding models, and the same prior supports scaffold-conditioned inverse folding without additional training.

World action models (WAMs) predict actions and future observations, typically from a reconstruction-based representation that carries noisy, redundant information which can complicate downstream predictions. We introduce LeWAM, a bidirectional transformer for forward, backward, inverse dynamics and policy prediction, on a decoder-free JEPA latent trained end-to-end through all four modes. We see the following benefits: 1) Alignment: linear probes read robot and object state from LeWAM's latent better than from a regular Le World Model (a forward-only JEPA world model), while the latent ignores visual distractors as well as LeWM does and far better than a reconstruction-based WAM. 2) Acting: Closed-loop evaluations of LeWAM match a regular flow-matching policy trained on the same encoder at matched size, while also providing a world model. 3) Planning: Sampling raw actions when planning with WAMs lets MPC exploit dynamics-model inaccuracies; planning in the noise space of the policy head instead improves the closed-loop performance of these WAMs.

Diffusion models have achieved remarkable success in image generation, yet tracing their outputs to individual training examples remains challenging. Existing attribution methods often compress factor-specific effects into scalar responses, making distinct internal changes indistinguishable. This is particularly limiting for diffusion models, where semantic factors emerge through evolving representation dynamics during denoising. We therefore reformulate diffusion data attribution as attributing factor-induced internal response trajectories. In this paper, we propose a novel Concept Attribution method through Dynamic Trajectories(CADT). We argue that attribution should therefore ask not only which examples matter, but also how their influence unfolds during generation. Specifically, we construct matched counterfactual pairs at identical noisy states to isolate factor-specific representation displacements, and model their directional and magnitude evolution across denoising as dynamic attribution signatures. For each training example and generated query, CADT extracts stage-wise feature vectors and integrates them along the denoising process to form a trajectory descriptor. Applying the same construction across the training set yields a bank of factor-specific trajectory descriptors. The covariance statistics of this bank are then used to construct . CADT uses this covariance-aware positive-semidefinite kernel to calibrate the query and training representations, and compares the calibrated query trajectory with each training trajectory to produce the final training-sample attribution scores. Experiments on multiple public datasets show consistent improvements over existing diffusion attribution baselines across hierarchical, compositional, and style attribution.

Causal video diffusion models generate video autoregressively, which suits streaming, interactive, and long-video generation. Under standard training, however, they often yield lower generation quality than bidirectional models of the same size. Many existing approaches address this gap by initializing from or distilling a pretrained bidirectional teacher. We instead train a causal model from an image-model initialization, with no bidirectional video model at any stage. Because this path requires neither a large bidirectional teacher nor a complex distillation pipeline, it is simpler and more scalable. On this path, we find that a causal model trained on ground-truth history becomes strongly dependent on it, so that at inference errors in its own generated history propagate forward. We hypothesize that much of this dependence is unnecessary, because the current input already determines much of what the history provides. We propose Conditional Residual Prediction (CRP), a simple recipe for reducing a model's reliance on a condition: the model first predicts the target without the condition, and the condition may only add a residual on top of this prediction. Applied to history, CRP makes the model predict each chunk from the present as far as it can and use the past only for what the present cannot supply. In controlled experiments, CRP nearly closes the 6.14-point gap to a bidirectional model trained under the same setup. Scaling this recipe, we train Optica, a 2B-parameter causal video model that autoregressively generates 5-second 480p videos and reaches 82.78 on VBench with only about 15M training videos.

Acquiring realistic microstructure data through Electron Backscatter Diffraction (EBSD) is costly and time consuming, often relying on specialised equipment. As microstructures strongly influence material properties, generating realistic samples is essential for modelling the behaviour of polycrystalline materials. We introduce a generative model for synthesising realistic polycrystalline microstructures using flow matching and graph neural networks. By representing microstructures as anisotropic power diagrams, our model learns a compact geometric parametrisation and can render generated samples at arbitrary pixel resolution. A $C_4$-equivariant architecture incorporates rotational symmetry directly into the model, ensuring that rotations of the input noise produce corresponding rotations of the generated microstructure. We also demonstrate how training-free guidance can be used to generate complex microstructures, based on user defined objective function. In particular, we generate microstructures resembling a copper weld, cast metal slab, 3D-printed stainless steel and heterogeneous lamella titanium.

Co-denoising pretrained representations such as DINO can substantially improve the training speed and quality of flow matching models, but it introduces a second denoising trajectory and requires carefully designed schedules. We propose a simpler alternative: predict the pretrained representation directly, then condition the model on its own prediction. This removes the need for a second ODE and any representation-specific denoising schedules, while retaining the benefits of representation guidance. Our approach converges substantially faster and achieves better generation quality as measured by FID score. On ImageNet, it outperforms the state of the art in latent space at 2x fewer epochs than prior methods; in pixel space, it improves FID over comparable prior methods by more than 20%. These results support a simple principle: do not denoise what you can predict. Our code is openly available at https://github.com/arijit-hub/dino_forcing.

In autonomous driving, understanding scene topology - the connectivity between lanes and traffic elements - is critical for safe path planning and motion control. While current methods excel at detecting individual map elements, their connectivity reasoning often falls short of its theoretical potential, leaving a significant performance gap relative to the theoretical upper-bound achievable given the underlying detections. Furthermore, the decision-ready topology graphs passed to downstream tasks often remain unreliable. Current approaches typically derive connectivity by thresholding continuous topology scores; however, these scores often fail to reflect the true logical likelihood of connectivity, resulting in false positives or missing connections. Existing benchmarks further overlook this issue by primarily evaluating continuous metrics, rather than assessing the discrete connectivity required for decision-making. To bridge these gaps, we propose TopoEnhance, a novel topology enhancement framework designed to unlock the latent potential of existing methods and improve the reliability of decision-ready topology. We formulate topology enhancement as a denoising-based reconstruction process, where the model learns to recover structural consistency from stochastically corrupted ground-truth graphs. This formulation enables the model to resolve logical inconsistencies and rectify unreliable connections, producing robust discrete topology graphs that closely approach theoretical maximum performance. Extensive experiments across different baselines show that TopoEnhance consistently improves both continuous topology metrics (TOP score), and discrete connectivity measured by our adapted Topology Jaccard Similarity (TJS) metric. As a flexible, source-agnostic framework, TopoEnhance delivers substantial gains across diverse state-of-the-art baselines without requiring retraining.

Diffusion and autoregression (AR) have long been seen as different categories of generative models, with diffusion specialising in continuous fields and AR specialising in discrete tokens. Recent work seeks to combine the advantages of the two models, and each hybrid fixes its decoding schedule by design. In this paper, we ask whether the performance of decoding schedules of one model can be predicted before decoding at a fixed number of steps. We describe diffusion, AR, and models in between as paths on one corruption lattice, and define the cost of a schedule as the dependence its parallel steps discard. The cost shows that the fewest steps of a zero-cost schedule are set by the geometry of the data, in the same way for tokens and for continuous fields. In particular, for data that are Markov on a graph and dependent along its paths, the fewest steps equal the graph's treedepth, which is logarithmic in the length of a sequence and linear in the side length of a grid. With fewer steps than the treedepth, every schedule pays a positive cost, whose ranking we predict before decoding with a kernel of pairwise dependence estimated from pretrained weights. Across text generation, image generation, and video generation, we verify most of the predictions about the rankings of different schedules under different metrics and benchmarks. This work therefore provides a design principle for decoding for future AR models, diffusion models, and anything in between. Our code is available at https://github.com/TSUITUENYUE/The-Lattice-of-Transition-Laws.

Generative conformal prediction builds uncertainty sets from samples of a conditional generator, which are efficient only when the samples represent the response distribution well. This can require many samples, each of which can be costly, as in large diffusion models and scientific simulators, so the sampling budget must be used efficiently. Existing methods draw the same number of samples at every input, wasting samples where the response distribution is simple and undersampling where it is complex, which inflates sets and leaves those inputs under-covered. We propose CASA (Conformal Adaptive Sample Allocation), which characterizes the marginal value of an additional sample and allocates samples across inputs to minimize the expected set size subject to marginal coverage and an average sampling budget. Theoretical analysis shows that adaptive allocation yields smaller sets than a fixed count at the same budget: a missed mode forces a radius that spans the gap between modes, and even oracle radius cannot compensate for it. On synthetic and real tasks, CASA produces substantially smaller sets at the same budget, often improves conditional coverage, and complements existing radius-adaptive methods.

Anchored Langevin dynamics (ALD) is useful for non-smooth sampling where the density of the target distribution is possibly non-differentiable and heavy-tailed; reflected anchored Langevin dynamics (RALD) can sample possibly non-differentiable target density on a constrained domain. In this paper, we propose and study non-reversible anchored Langevin dynamics (NALD) for sampling possibly non-differentiable and heavy-tailed target density in the Euclidean space and the non-reversible reflected anchored Langevin dynamics (NRALD) for sampling possibly non-differentiable target density in the constrained space. Our construction adds a circulation drift generated by a possibly state-dependent divergence-free skew-symmetric matrix field and a stream potential. It preserves the target distribution without requiring derivatives of target density, admits a random-time-change representation, and applies both on the whole Euclidean space and on bounded domains with normal reflection. By breaking reversibility, we show that NALD and NRALD can converge to their target distributions faster than their reversible counterparts via finite-time non-asymptotic convergence analysis, a large deviations analysis and asymptotic variance reduction. Numerical experiments demonstrate the efficiency of the proposed algorithms.

Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin--Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.

Unified atomistic modeling has the potential to accelerate discovery in chemistry, materials science, and biology by bridging data-rich chemical domains and data-scarce biological contexts. However, existing generative approaches to atomistic modeling remain highly specialized to scientific disciplines (chemistry vs. biology) or do not leverage both high-volume organic (molecule) and inorganic (material) data for general-purpose pretraining. To this end, we introduce Zatom-2, an atomistic generative model pretrained on approximately five million structures from the OMol25 and OMat24 electronic structure datasets. Zatom-2 features a multiscale Transformer architecture coupled with conditional flow matching that supports force conditioning and foundational pretraining tasks such as generation, structure prediction, and prediction of molecular and material energies and forces. Empirically, Zatom-2 achieves better molecular distribution fidelity than Zatom-1 and achieves strong performance on existing molecule and material generation benchmarks. Zatom-2 demonstrates the ability to control sample generation across low- and high-force regimes, and enhances protein generation in a low-data setting through joint generative-predictive pretraining and transfer learning, increasing protein backbone designability in a length extrapolation setting from 67.8% without pretraining to 74.8% after finetuning on 2,000 protein domains.

Generative diffusion models are well-suited for probabilistic precipitation nowcasting, but existing approaches often rely on separately trained compression or deterministic forecasting components and remain costly at inference due to iterative denoising. We introduce Just Weather Scoring (JWS), a single-stage, end-to-end diffusion model which addresses both issues by forecasting directly in radar space and enabling few-step generation. Radar-space modeling greatly simplifies training and inference and eliminates uncertainty arising from lossy compression. JWS combines Masked Asynchronous Diffusion, a timestep-sampling scheme that preserves clean context while adapting diffusion training to high-dimensional spatio-temporal data, with a simple scoring-rule objective that aligns training with probabilistic forecasting and unlocks few-step generation. On the SEVIR and MeteoNet benchmarks, JWS achieves state-of-the-art probabilistic forecasting performance at reduced training and inference cost. Even our smallest model remains competitive using substantially fewer parameters and more than 17x faster inference.

Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning. At a symmetry-breaking bifurcation, a single input admits multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogates. We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems. Bi-FORK generates complete trajectories through latent flow matching, preserving space and time coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized pass. We evaluate Bi-FORK on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, spanning continuous, discrete, and field-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers the multimodal solution structure while scaling several orders of magnitude beyond prior approaches, opening generative modeling to high-dimensional bifurcating physical systems.

Diffusion models can represent complex, multimodal trajectory distributions, but extracting uncertainty from them typically requires costly Monte Carlo sampling. This limits their use in real-time control, where robots must rapidly assess risk and maintain safety margins. We introduce Score-Curvature for Online Precision Estimation (SCOPE), a lightweight module that augments diffusion trajectory models with control-ready uncertainty. SCOPE learns a structured precision matrix around each nominal trajectory by distilling score-curvature information and producing calibrated Gaussian tubes with low overhead and without repeated Monte Carlo sampling. These tubes provide per-timestep covariance estimates that can be used both as predicted occupancy for moving agents and as adaptive exploration guides for robot control. We evaluate SCOPE with mode-conditioned multimodal diffusion backbones in pedestrian forecasting, crowd navigation, Maze2D control, and real-world Franka Panda manipulation. Across these settings, SCOPE provides fast uncertainty estimation, which leads to better closed-loop performance. Project page: https://zackaxue.github.io/SCOPE-project-page/

Prompt learning is a popular method for adapting foundation models, but learned prompts are typically task-specific and fail to generalize to new classes, domains, or compositions of tasks. In this paper, we introduce a Diffusion Meta-Prompt (DMP) model , a framework that models the distribution of learned prompts using diffusion models. Given a repository of previously learned prompts, DMP is trained and sampled without access to the original task examples or task losses, and synthesizes new prompts conditioned on natural language task descriptions. To improve the sampling stability, we introduce a test-time steering strategy for DMP, which uses the best training-selected prompt in the repository as a latent anchor during diffusion sampling, without retraining the DMP or accessing test classes. DMP improves generalization across classification, retrieval and text-to-image generation tasks, supports concept composition and negative prompting without explicit training. It reduces storage and inference costs by over 90% compared to prompt retrieval methods. For composite classification, DMP achieves upto 2.0% average gain over prior meta-learning methods across 55 pairs of datasets with gains as high as 8.5% on specific pairs such as Eurosat and Flowers. DMP also enhances cross-task generalization with ~2-9% improvement for hierarchical classification task. We further provide a theoretical guarantee bounding the expected task loss of prompts sampled from a DMP. Code is available: https://github.com/DeepakSridhar/dmp

Conditional diffusion models generate diverse, novel, and high-quality samples under prescribed conditions. However, theoretical understanding of their memorization and generalization remains limited, while recent works have characterized these behaviors primarily in unconditional settings. In this work, we analyze a random-feature conditional score model in the high-dimensional proportional limit, deriving asymptotic expressions for training and test losses. By decomposing the test loss, we show that in the overparameterized regime, increasing model width improves prediction of the condition-dependent mean while reducing within-condition prediction variance, a phenomenon we term "malign generalization." Furthermore, analyzing the training loss reveals that more informative conditions lead to memorization of training samples at smaller widths. These theoretical findings are supported by experiments with U-Net architectures on realistic data.

Diffusion models have achieved remarkable success in generative modeling, with their sampling procedures routinely modified to control generation and improve efficiency. These modifications introduce perturbations along the sampling trajectory, raising a central question: how do such perturbations affect generated output? To address this question, we develop a theoretical framework to investigate perturbation propagation, combining dynamical analysis of the sampling process with an information-theoretic characterization of output responses. Within this framework, we quantify perturbation strength using the Kullback--Leibler (KL) divergence between perturbed and reference trajectory distributions, termed as path cost, which is shown to bound, but do not determine, changes in the output distribution. Building on this analysis, we derive a response identity that connects the propagation and accumulation of local perturbations with the information captured by a selected feature mean, explaining why changes in the output distribution can remain undetected by its first-order response. We test our theoretical analysis through controlled interventions at equal path cost in pretrained diffusion models, revealing distinct patterns of output sensitivity across sampling stages and spatial frequencies. To assess whether our framework can diagnose perturbations arising from practical approximations, we apply it to cache-based acceleration and show that our propagation analysis reliably identifies sampling intervals where caching causes larger image errors.

Flow matching has emerged as a scalable paradigm for training high-quality generative models, but sampling from the learned probability flow requires many network evaluations. Distillation can reduce this cost to one or a few evaluations; however, one-step generation often sacrifices quality, making few-step generation the practical operating regime. Existing few-step methods perform their iterative computation along the probability flow and therefore require a fixed, manually chosen timestep discretization. This discretization is often chosen heuristically and is expensive to tune; it may also be restrictive when refinement difficulty differs across samples or spatial locations. We introduce data-space iteration, a few-step generation framework that removes flow discretization altogether. Starting from noise, a shared generator directly refines its prediction in data space, with every iteration trained to produce the best sample permitted by its capacity. Our formulation integrates with distribution matching distillation (DMD) with minimal changes, enabling a controlled comparison between iteration methods under matched training settings. On class-conditional ImageNet 256x256, data-space iteration outperforms standard discretization baselines and matches or improves upon variants selected through schedule search, without requiring schedule-specific training. These results show that data-space iteration provides a simple and effective alternative to discretized flow-space iteration for fast generation.

Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear. In this work, we leverage Gaussian distributions to isolate this phenomenon. We establish 2-Wasserstein convergence bounds for optimized hyperparameters, showing that diffusion processes achieve a sampling error of $O(\sqrt{dλ_{\max}}\log N/N)$, where $d$ is the dimension, $N$ the number of sampling steps, and $λ_{\max}$ the largest eigenvalue of the target covariance matrix. Unadjusted and underdamped Langevin dynamics suffer from an additional $\sqrtκ$ factor, where $κ$ is the condition number. These rates follow from spectral bounds which are sharp: we confirm them via matching first-order asymptotics as $N\rightarrow\infty$. Our analysis provides a rigorous characterization, in the Gaussian setting, of how time-dependent score trajectories remove condition-number dependence during sampling. By contrast, in the learning phase, we show that estimating the unnoised score by gradient descent leads to essentially the same estimator as estimating a noisy score, which suggests that the benefits of noising do not come from the learning phase.

Diffusion models generalize early in training and later reproduce individual training samples. Standard tests detect memorization only once one-shot generation produces near-copies, leaving a released model unaudited until its outputs fail. We show that memorization is encoded in the geometry of the learned energy landscape before it appears in generated samples, a state we call latent memorization. Using score divergence and basin volume, we find that localized basins form around training samples and separate them from held-out samples before the first memorized sample appears, with an onset that follows the same $O(n)$ scaling as the memorization time. We probe these basins with cyclic denoising, which repeatedly applies partial noising and denoising. Under the exact empirical score, we prove that cycling started near an isolated training sample recovers it and returns to it over any finite number of cycles with high probability. In trained models, cycling recovers training images from CelebA and CIFAR-10 checkpoints whose one-shot samples contain no copies, and at a CelebA checkpoint with 0.1% one-shot copies, 500 cycles raise the memorized fraction above 30%. Cycling also reveals degenerate attractors that match no single training image and fade as training proceeds, so residence in a basin does not by itself imply memorization. These findings hold on a Gaussian mixture, CelebA, and CIFAR-10 across optimizers, architectures, noise schedules, and training-set sizes, and extend to off-the-shelf Stable Diffusion v1.4, where the cycled conditional-unconditional divergence gap separates memorized from non-memorized prompts with an AUC of 0.944 and a TPR of 0.866 at 1% FPR. More broadly, what a diffusion model has memorized is a property of the geometry and stability of its learned distribution, and assessing it requires examining this structure rather than generated outputs alone.

Binary diffusion models typically require a large number of function evaluations (NFEs) to generate high-quality samples, making practical inference computationally expensive. Reducing NFEs while preserving sample quality without distillation or additional training remains a significant challenge. Existing binary diffusion models define a discrete one-step forward path and then derive the reverse posterior. In low-NFE settings requiring cross-step sampling, they approximate the true multi-step likelihood with a single-step likelihood transition, which severely degrades sample quality. To address this fundamental limitation and decouple the generative dynamics from fixed discrete time steps, we propose Bernoulli Flow Models (BFM). Rather than relying on sequential one-step Markov diffusion chains, BFM defines a unified continuous global Bernoulli probability flow path between data distributions and pure noise, from which we derive analytical closed-form posterior transitions over arbitrary time intervals. Consequently, reducing the inference NFE is no longer an approximation based on skipping discrete steps; it only requires re-evaluating the analytical posterior over a new time grid. This eliminates the structural training-inference mismatch inherent to discrete chains and yields self-consistent low-NFE sampling. Experiments show that BFM is highly robust to aggressive NFE reduction. On LSUN Churches 256x256, a BFM trained with 256 steps achieves an FID of 9.22 using only 16 sampling steps, whereas the state-of-the-art discrete baseline degrades to 204.10. BFM also remains competitive with continuous and discrete generative baselines under standard full-step inference. These results establish BFM as a theoretically rigorous, self-consistent, and practically effective framework for fast binary data generation.

We introduce RefineMix, a framework for training discrete diffusion models under severe data scarcity, a common constraint in scientific applications. RefineMix uses out-of-distribution data at selected diffusion times to improve generalization without biasing the sampling distribution. Although this strategy has been explored in continuous diffusion, discrete diffusion presents a distinct challenge: unlike Gaussian noise, masking preserves domain information in surviving tokens, limiting the use of related data at high noise levels. At low noise levels, however, the domains effectively disjoint supports become an advantage, allowing the model to learn from both in-domain and out-of-distribution data without biasing the sampler. We formalize these intuitions and provide a theoretical analysis for the proposed method. Experimentally, across five domain-shift settings, RefineMix matches or outperforms in-domain finetuning and data mixing. For protein sequence generation, finetuning with just 197 in-domain examples nearly doubles the fraction of generated proteins that are simultaneously novel, foldable, and in-family compared to standard finetuning.

Text-to-image diffusion models are increasingly distilled into few-step variants and being deployed to enable fast inference. However, their ability to generate harmful or undesired content poses significant safety risks. Data-driven unlearning methods suppress targeted generations by fine-tuning model weights using specialized unlearning objectives. Crucially, these objectives implicitly rely on multi-step denoising dynamics, an assumption that breaks down for few-step distilled (FSD) models, resulting in ineffective forgetting. Furthermore, performing unlearning on the non-distilled base model and subsequently re-distilling it to obtain an unlearned FSD model incurs substantial computational and time overhead, making it impractical in many settings. Hence, we address this limitation with a preference-driven unlearning framework that revisits Direct Preference Optimization (DPO) for diffusion models. We show that standard DPO and its unlearning derivatives, formulated around noise-prediction error, transfer poorly to FSD models due to their altered generation dynamics. To overcome this, we introduce a modified preference optimization formulation explicitly aligned with the few-step generation properties, enabling direct concept removal in FSD models while preserving few-step efficiency and maintaining strong retention of desirable (non-targeted) capabilities. We evaluate our framework primarily on identity and NSFW (nudity) removal tasks and also extend our method to object-level unlearning. Extensive experiments demonstrate consistent and effective forgetting, and strong retention performance, establishing our method as a practical and principled solution for unlearning in FSD models.

Estimating the symbolic or analytical form of probability density functions (PDFs) from observed samples is a fundamental challenge in statistical and computational modelling. This process is critical for deriving interpretable and generalizable relationships characterizing the underlying phenomenon. Traditionally, this estimation depends strongly on domain expertise and prior field-specific knowledge, with experts selecting appropriate functional forms or parametric families based on empirical evidence and theoretical understanding. The coefficients of these forms are then typically determined through parameter estimation. In this paper, we develop a framework for estimating symbolic expressions of unnormalized distributions from observed samples using domain-specific prior knowledge, such as the range of interactions and a predefined set of primitive functions. We integrate deep generative models with symbolic regression (SR), incorporating inductive biases, such as factorizing large distributions, to keep the problem tractable. The deep generative models we examine include likelihood-based models, viz., flow models, and score-based models. Experiments show the effectiveness of the proposed framework for estimating density functions for multivariate toy distributions as well as lattices from computational physics, namely, XY model and $φ^4$ theory. When applied to the renormalization problem in $φ^4$ theory, the proposed framework estimates compact symbolic approximations of the hamiltonian function at different scales directly from samples, yielding expressions that may be challenging to derive using traditional perturbative or analytic approaches in nonperturbative settings.

Motivated by recent applications in generative modeling and sampling, we introduce a framework for optimal measure transport where cost captures the notion of neural network complexity. In transport-based generative models, samples from a reference distribution (e.g. Gaussian) are mapped to samples of a target distribution along ordinary or stochastic differential equations. These are implemented as deep residual networks when discretized in time, where each hidden layer approximates the associated instantaneous velocity. Thus, given a pair of target and reference measures, a natural question is to search for the most efficient neural representation that implements this transport. Our starting point is the kinetic formulation of OT, due to Benamou and Brenier. We replace the average kinetic $L^2$ energy by the Barron energy \cite{bach2017breaking, ma2022barron}, a natural norm which measures the complexity of representing a given vector field with a neural hidden layer, and which captures the adaptive properties of feature learning. This defines a metric on the space of probability measures, complementing existing Wasserstein and Stein geometries. In this work we examine the properties of this metric in the context of generative modeling. As a first application, we quantify the suboptimality of diffusion generative modeling in the Barron geometry by establishing super-polynomial score approximation lower bounds for data generated by neural network pushforwards of the Gaussian. We then investigate the benefit of adaptivity as a way to study alternative generative models. In a companion paper \cite{companionpaper} we leverage the Barron transport geometry for sampling applications, extending the scope of Stein variational gradient methods via feature adaptation.

Unlike autoregressive models, discrete diffusion-based models for zero-shot text-to-speech generate speech tokens in parallel and can revisit earlier predictions. Mask-and-replace training extends mask-only training by randomly replacing some tokens, and its gains are commonly attributed to self-correction, the ability to revise previously generated tokens. However, exposure to randomly perturbed context during training may itself improve generation, raising the question of whether these gains require inference-time token revision. To investigate this question, we use DeMaR, which combines mask-and-replace training with confidence-ranked mask-only sampling while preserving the total training corruption probability. Trained from scratch on LibriTTS, DeMaR achieves lower word error rates (WER) than autoregressive and mask-only diffusion baselines using the same speech tokenizer. This advantage persists when each token remains unchanged after first being unmasked. Matched training conditions on two heterogeneous speech tokenizers show that both noisy-context augmentation and replacement supervision improve WER under this restriction. These findings demonstrate training-side benefits of replacement beyond enabling inference-time token revision.

Cine cardiovascular magnetic resonance (CMR) analysis relies on multi-frame sequences capturing the full cardiac cycle. However, standard multi-frame acquisition depends heavily on electrocardiogram (ECG) gating and repeated breath-holds, posing challenges in uncooperative populations, resource-limited settings, and temporally corrupted datasets. Existing methods that synthesize full cardiac sequences either rely on explicit ECG signals to parameterize myocardium function, or employ deformable registration without physiological constraints, failing to faithfully reproduce clinically relevant dynamic metrics such as ejection fraction (EF) and ventricular contraction magnitude. We present PhaseFlow, a unified generative framework that overcomes both limitations. PhaseFlow estimates a non-linear cardiac phase signal directly from the input sequence via a segmentation-derived left-ventricular (LV) area curve, capturing the asymmetric dynamics of systole and diastole without any ECG dependency. At inference, this phase signal is provided by a pathology-specific template, informing phase-specific frame generation. A rectified flow model conditioned on the phase and slice position synthesizes the full cardiac motion trajectory in the latent space, decoded into a diffeomorphic displacement field that warps end-diastole pixel intensities directly, eliminating the reconstruction blur often accompanying the variational autoencoder. On the ACDC benchmark, PhaseFlow achieves superior physiological fidelity and image realism, with best LV volume curve $R^2$, structural similarity (SSIM) and generative quality (FID) among all baselines. Ablation studies confirm that each proposed component contributes measurably to the overall performance.

Generative models are increasingly trained in self-consuming iterative loops, where users curate preferred samples from model-generated candidates and the curated samples are used to train future generations of the model. Prior work has largely assumed fixed user preferences, but in practice exposure to model outputs gradually reshapes what users perceive as desirable, creating a feedback loop in which model distributions and user preferences co-evolve. We take a first step toward understanding the long-term behavior of such coupled dynamics. We show that when training relies entirely on user-curated synthetic data, iterative curation amplifies initial biases and drives the system toward one of multiple singleton equilibria in which the instance holding an initial advantage eventually dominates. In contrast, injecting reference data into training at a sufficiently large rate fundamentally changes the dynamics and yields a unique globally attracting equilibrium. Building on this insight, we study how reference-data injection can be used to control long-term outcomes, and propose an efficient algorithm that jointly selects a reference distribution and its mixing weight to steer the coupled system toward equilibria that preserve desired attributes while minimizing data collection costs.