Implicit Generative Modeling

Implicit generative models based on deep neural networks have revolutionized many scientific fields, from weather research to language generation. They successfully model complex random objects arising in real-world problems. In this work, we propose a sample-efficient training mechanism for these models. Our approach leverages regularized inference with shrinkage priors and generalized Bayes. In the large $p$ (parameter dimension) and small $n$ (sample size) setting, sparsity-inducing priors have been successfully used for linear regression when $p \gg n$. However, their application to implicit generative models remains challenging due to the intractability of the likelihood function. To address this, we adapt a scoring rule posterior based on a strictly proper scoring rule, following the generalized Bayes framework. We then propose a block SGMCMC within Gibbs sampling mechanism. This enables efficient exploration of high-dimensional parameter spaces by identifying a sparse representation of neural implicit generative models. We demonstrate the performance of our proposed method through experiments on $p \gg n$ linear regression and an application of neural generative models.

Seeded noise lets games generate any region of an unbounded world on demand. We ask what such a generator needs when every small window must come from one example, the constraint behind Wave Function Collapse. The difficulty is that local constraints can require agreement over arbitrary distances: in a brick wall, each row keeps its place between the mortar lines. We study local generators, each cell a fixed function of the randomness near it. When the constraints carry a quantity that varies across the example, no generator that applies one rule, ignoring position, to independent randomness at every cell can be both exactly valid and faithful to the example's statistics, however far each cell reads. At radius r, staying faithful forces forbidden windows at a density of at least order 1/r, and a construction attains this order. To vary the quantity between exactly valid worlds, a generator needs randomness shared along its direction. We give a finitely checkable condition under which row types drawn from the seed and the position modulo a fixed period suffice for exact validity without learning. A search over the example's patches certifies these quantities and names the input each needs. Across 52 public examples of Wave Function Collapse and 27 from other implementations, it certifies only examples where a learned generator on independent randomness stays far from valid after repair. Given that input, a neural cellular automaton and a diffusion model become valid on 10 and 8 of the 12 certified examples that receive one, and on none from independent randomness. Valid means at most one forbidden window in a thousand after repair. With octaves of seeded noise elsewhere, the automaton is valid on 45 of the 52 public examples and 21 of the 27 from other implementations, and repair keeps random access.

Mutual information (MI) provides an objective for suppressing or encouraging statistical dependence in implicit generative models. However, direct MI evaluation is challenging in implicit models due to typically intractable densities. A remedy is estimating the generator gradient from the difference between conditional and marginal scores. This score difference can, in turn, be estimated by differentiating a log density ratio learned through classification. This construction nevertheless faces two difficulties: (i) singular distributions need not admit the required score functions, and (ii) poor overlap can hinder density-ratio estimation. We therefore introduce Spread Mutual Information (SMI), a weighted integral of MI across noise levels obtained by applying a common spreading kernel to the generated variable. Gaussian spreading yields smooth, strictly positive conditional and marginal densities, extending the gradient construction to distributions that may originally be singular. Across a variaty of experiments, SMI consistently achieves effective dependence control among MI-based methods and remains competitive with established task-specific approaches.

Despite their remarkable success in modeling complex data, generative models face a fundamental tradeoff. Global approaches can capture full structural coherence but suffer from high computational costs, while local models are efficient but often fail to reproduce long-range correlations and global coherence. The renormalization group (RG) bridges this gap by seamlessly connecting spatial structures across different length scales, retaining quasi-local descriptions at each step while preserving long-range correlations. We introduce renormalization group flow matching (RGFM), a generative framework that systematically structures data generation across different spatial scales. By using an exact RG flow as the probability path, RGFM progressively generates data from long- to short-wavelength structures. To reconcile scalability with global structure, we exploit two key properties of the RG: quasi-locality and scale separation. We rigorously show that the RGFM probability flow can be accurately approximated by local velocity fields acting over a spatial range $O(Λ^{-1}[\ln L+\ln(1/\varepsilon)])$ for RG wavenumber scale $Λ$, linear system size $L$, and prescribed error tolerance $\varepsilon$. This property enables local generative modeling with patches of size $O(\ln L)$ and a computational cost that scales nearly linearly with the system volume. We numerically demonstrate that local RGFM reproduces long-range correlations far beyond its receptive field in representative one-dimensional distributions, while conventional local flow matching exhibits substantial errors at long distances. On FFHQ images, RGFM yields far more coherent and higher-quality samples than local flow matching at 64x64 and 256x256. Our results establish RG-guided probability flows as a promising route toward scalable generative modeling that captures long-range structure using only local computation.

Safety-critical traffic scenario generation is essential for evaluating autonomous driving systems under rare but high-risk interactions. Existing diffusion-based methods offer strong controllability in closed-loop generation, but their iterative denoising process is computationally expensive and may accumulate sampling and guidance errors over long rollouts, causing unrealistic motion artifacts such as abnormal acceleration and off-road behavior. To address these issues, we propose RiskFlow, a closed-loop safety-critical traffic generation framework that reformulates future behavior generation as one-step flow transport in the action space during training. At test time, RiskFlow generates safety-critical interactions through a selective guidance procedure in which time-to-collision-based critical-agent ranking selects high-risk agents and an adversarial interaction objective directly refines their output actions. Vehicle-dynamics rollout and map-aware regularization then translate guided actions into feasible trajectories while discouraging off-road behavior. By intervening on selected agents in the output space, RiskFlow avoids repeated corrections of intermediate denoising states, thereby mitigating accumulated guidance errors and accelerating closed-loop scenario generation. Experiments on the nuScenes dataset under closed-loop evaluation show that RiskFlow achieves a strong adversariality-realism trade-off across multi-agent and long-horizon settings. Compared with representative baselines, RiskFlow consistently improves realism while maintaining competitive safety-critical generation capability, and substantially reduces inference time for evaluation.

The use of synthetic data in machine learning applications and research offers many benefits, including performance improvements through data augmentation and privacy preservation of original samples. This work proposes an efficient synthetic data generation method based on a fully connected neural network that transforms a high-dimensional random Gaussian distribution to approximate a target real-world dataset. The proposed solution combines data preprocessing designed for tabular data with distribution modeling and PCA dimensionality reduction to further enhance data privacy. The work also defines two dedicated randomized loss functions based on Wasserstein distance combined with feature Covariance and a randomized pairwise error reduction loss function. The experiments conducted on 25 diverse tabular real-world datasets confirm that the proposed solution obtains similarity and privacy scores relative to the state-of-the-art generative methods and achieves reference MMD scores orders of magnitude faster than modern deep learning solutions. The experiments involved analyzing distributional similarity, privacy protection, and the utility of synthetic data in classification tasks.

Existing generative models, such as diffusion and auto-regressive networks, are inherently static, relying on a fixed set of pretrained parameters to handle all inputs. In contrast, humans flexibly adapt their internal generative representations to each perceptual or imaginative context. Inspired by this capability, we introduce Composer, a new paradigm for adaptive generative modeling based on test-time instance-specific parameter composition. Composer generates input-conditioned parameter adaptations at inference time, which are injected into the pretrained model's weights, enabling per-input specialization without fine-tuning or retraining. Adaptation occurs once prior to multi-step generation, yielding higher-quality, context-aware outputs with minimal computational and memory overhead. Experiments show that Composer substantially improves performance across diverse generative models and use cases, including lightweight/quantized models and test-time scaling. By leveraging input-aware parameter composition, Composer establishes a new paradigm for designing generative models that dynamically adapt to each input, moving beyond static parameterization.

Many generative tasks in chemistry and science involve distributions invariant to group symmetries (e.g., permutation and rotation). A common strategy enforces invariance and equivariance through architectural constraints such as equivariant denoisers and invariant priors. In this paper, we challenge this tradition through the alternative canonicalization perspective: first map each sample to an orbit representative with a canonical pose or order, train an unconstrained (non-equivariant) diffusion or flow model on the canonical slice, and finally recover the invariant distribution by sampling a random symmetry transform at generation time. Building on a formal quotient-space perspective, our work provides a comprehensive theory of canonical diffusion by proving: (i) the correctness, universality and superior expressivity of canonical generative models over invariant targets; (ii) canonicalization accelerates training by removing diffusion score complexity induced by group mixtures and reducing conditional variance in flow matching. We then show that aligned priors and optimal transport act complementarily with canonicalization and further improves training efficiency. We instantiate the framework for molecular graph generation under $S_n \times SE(3)$ symmetries. By leveraging geometric spectra-based canonicalization and mild positional encodings, canonical diffusion significantly outperforms equivariant baselines in 3D molecule generation tasks, with similar or even less computation. Moreover, with a novel architecture Canon, CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.