The paper establishes a reverse-time quantum diffusion framework that generates complex quantum ensembles from simple distributions by deriving and learning a feedback Hamiltonian from forward trajectory data.
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Score-Based Generative Modeling through Stochastic Differential Equations
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abstract
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
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- abstract Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate
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citing papers explorer
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Generative Modeling with Flux Matching
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
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How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
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Quotient-Space Diffusion Models
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Query Lower Bounds for Diffusion Sampling
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
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Denoising Diffusion Implicit Models
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
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Set Diffusion: Interpolating Token Orderings Between Autoregression and Diffusion for Fast and Flexible Decoding
Set diffusion factorizes likelihood over arbitrary token sets and uses a set-causal diffusion architecture to support KV caching and any-order decoding, yielding improved speed-quality tradeoffs versus prior diffusion LMs.
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Diffeomorphic Optimization
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
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Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition
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Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias
ReMatch corrects train-test residual distribution mismatch in probabilistic downscaling via optimal transport in low-dimensional PCA space, reducing under-dispersion and improving SSR and CRPS on HRRR-ERA5 wind data.
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Volterra Generative Models
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Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
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Drifting Preference Optimization for One-Step Generative Models
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Spectral Guidance for Flexible and Efficient Control of Diffusion Models
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Parameter-Efficient Generative Modeling with Controlled Vector Fields
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Generative Modeling by Value-Driven Transport
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CAdam: Context-Adaptive Moment Estimation for 3D Gaussian Densification in Generative Distillation
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On the Approximation Complexity of Matrix Product Operator Born Machines
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Kurtosis-Guided Denoising Score Matching for Tabular Anomaly Detection
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Guiding Distribution Matching Distillation with Gradient-Based Reinforcement Learning
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Diffusion Models Beat GANs on Image Synthesis
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Optimizing Visual Generative Models via Distribution-wise Rewards
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Decision-Aware Training for Sample-Based Generative Models
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Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps
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Class-frequency Guided Noise Schedule for Diffusion Models
Proposes CFRG noise schedule for diffusion models that assigns larger noises to low-frequency classes to improve generation on imbalanced datasets.
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VideoMDM: Towards 3D Human Motion Generation From 2D Supervision
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Least-Action-Guided Diffusion for Physical Extrapolation
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