QTD integrates quantization with diffusion for efficient data generation.
problem Challenges in continuous diffusion models, especially long-range transitions and biases.
method Quantized Transition Diffusion (QTD) integrates data quantization with discrete diffusion dynamics.
result QTD achieves efficient data generation with minimal score evaluations.
Study quantizes energy distribution in inhomogeneous phase transitions.
problem Quantifying energy distribution in inhomogeneous Allen-Cahn phase transitions.
method Analysis of varifolds and convergence of integer rectifiable varifolds.
result Equidistribution of energy between Dirichlet and Potential energy in phase field limit.
We study the dependence of geometric quantization of the standard symplectic torus on the choice of invariant polarization. Real and mixed polarizations are interpreted as degenerate complex structures. Using a weak version of the equations of covariant constancy, and the Weil-Brezin expansion to describe distributiona…
Faster sampling in discrete diffusion models with predetermined transition time.
problem Efficiency in sampling discrete diffusion models.
method Discrete Non-Markov Diffusion Models (DNDM) with predetermined transition time.
result Significantly reduces the number of function evaluations for faster sampling.
Optimal quantization improves dataset distillation for faster training.
problem Efficiently train models with synthetic data.
method Reformulate disentangled methods as optimal quantization problems.
result Better performance and generalization on ImageNet-1K and subsets.
QDSB accelerates Schrödinger bridge learning with quantized approximations.
problem Learning generative models from unpaired samples.
method Quantized diffusion Schrödinger bridges (QDSB) using anchor-quantized distributions and cell-wise sampling.
result QDSB achieves sample quality similar to existing methods but with significantly less computational time.
Paper models transition risk using jump-diffusion model to price credit swaps.
problem Capturing transition risk in financial markets.
method Calibrated jump-diffusion model to CDS term structure, using quantile regression.
result Jump-diffusion model captures transition risk, jumps represent green policies.
Discrete diffusion models improve text and image inference.
problem Challenges in posterior sampling with discrete diffusion models.
method Anchored Posterior Sampling (APS) with quantized expectation and anchored remasking.
result APS achieves state-of-the-art performance on various tasks.
Diffusion maps help learn complex quantum phase transitions from data.
problem Learning quantum phase transitions from experimental data is challenging.
method Diffusion maps for nonlinear dimensionality reduction and spectral clustering.
result Diffusion maps can learn complex phase transitions unsupervised.
Diffusion models reveal a phase transition in reconstructing high-level features.
problem Understanding the hierarchical structure of natural data.
method Study of hierarchical generative models of data using diffusion models.
result The backward diffusion process shows a phase transition at a threshold time, where high-level features suddenly drop in reconstructibility.
Study phase transitions with prescribed mean curvature in Riemannian manifolds.
problem Understanding phase transitions with prescribed mean curvature in geometric settings.
method Analyzing solutions to inhomogeneous semilinear elliptic PDEs, establishing bounds and asymptotics.
result Established upper and lower bounds for eigenvalues of phase transition problems.
Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.
problem Understanding the performance and capabilities of generative diffusion models.
method Reformulating generative diffusion models using statistical mechanics, focusing on phase transitions and symmetry breaking.
result Generative diffusion models undergo second-order phase transitions with mean-field universality, critical instability, and mean-field critical exponents.
Combines deep state space models with diffusion models for better forecasting and capturing latent dynamics
problem Forecasting and capturing latent dynamics in time series
method DDSSM: Diffusion-driven state space model
result Empirically outperforms state-of-the-art deep SSM
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if not most, contemporary modelling approaches for future technology pathways overlo…
Entropy tracking reveals class commitment transitions in diffusion models.
problem Diffusion models lack reliable methods to detect semantic structure transitions.
method Tracking class-conditional entropy of latent variables.
result Entropy isolates noise regimes critical for semantic structure formation.
Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
A new model trains prior and encoder/decoder networks simultaneously for efficient generation.
problem Complex autoregressive prior in VQ-VAE models leads to slow generation.
method Builds a diffusion bridge between continuous and non-informative prior distributions.
result Model is competitive and efficient in optimization and sampling.
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.
problem Approximating manifold heat semigroups from graph data under low regularity conditions.
method Iterating graph transition matrix P to approximate Qt=etΔ, bounding error in ∞-norm. result Convergence rates O(N−2/(d+6)) for manifold heat semigroup approximation, valid for in-sample and out-of-sample. AIS corrects rollout-training mismatch in quantized RL, improving speed and stability.
problem Rollout-training mismatch in quantized RL causes bias and training collapse.
method Adaptive Importance Sampling (AIS) adjusts gradient correction per batch.
result AIS matches BF16 baseline on most tasks while improving speed.
GLASS Flows improves flow and diffusion model performance by optimizing sampling efficiency.
problem Efficiency bottleneck in sampling Markov transitions for flow and diffusion models.
method Introduces GLASS Flows, a new sampling paradigm that simulates a 'flow matching model within a flow matching model' to sample Markov transitions efficiently.
result Eliminates the trade-off between stochastic evolution and efficiency in large-scale text-to-image models.
TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.
problem Improving the convergence of Denoising Diffusion Probabilistic Models.
method Critically damping the Third-Order Langevin Dynamics (TOLD) forward transition matrix using eigen-analysis.
result TOLD++ converges faster than TOLD, verified on toy and real datasets.
Paper analyzes latent space geometry in generative models using Fisher information.
problem Understanding the structure of latent spaces in generative models.
method Reconstructs Fisher information metric from generated samples and posterior distribution.
result Reveals fractal structure and abrupt changes in Fisher metric at phase boundaries.
Develops diffusion models for time-varying correlation on the circle.
problem Time-varying correlation modeling on the circle.
method Stochastic processes on the unit circle, specifically Brownian motion and von Mises diffusion.
result Derives an accurate analytical approximation to the transition density of the von Mises diffusion.
Construct geometric interpretation of Heston model using group quantization.
problem Geometric interpretation of Heston model
method Lifted local Lie groupoid formulation
result Geometric interpretation of Heston pricing operator and Riccati equations
New method preserves spectral clustering performance under aggressive sparsification and quantization.
problem Maintaining spectral clustering performance with sparse and quantized data.
method Random matrix theory applied to eigenspectrum changes under sparsification and quantization.
result Spectral clustering performance is preserved even with aggressive sparsification and quantization.
GLAD improves latent graph generation by quantizing discrete latent space.
problem Latent space graph generative models lack performance and make unnatural assumptions.
method Adapting diffusion bridges to a discrete latent space, avoiding data space decompositions.
result GLAD achieves competitive performance on graph benchmark datasets.
Paper introduces TtT, market-implied transition time, from greenium term structure.
problem Estimating market-implied transition time to a low-carbon economy.
method Develops inference theory for TtT, introduces two stochastic models.
result Combines two-layer analysis for consistent estimation of diffusion parameters.
Paper analyzes LPSA algorithm for constrained optimization, revealing phase transitions and bias-variance trade-offs.
problem Optimization problems with linear constraints.
method Loopless projection stochastic approximation (LPSA) with jump diffusion approximation.
result LPSA trajectories converge to SDEs, revealing asymptotic behaviors and phase transitions.
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of f…
A new method for training diffusion models using likelihood matching.
problem Training efficient and accurate diffusion models.
method Likelihood Matching approach, quasi-likelihood approximation, score and Hessian estimation.
result Consistent matching of first two transitional moments between diffusion steps.
New protocols show 1-bit mean estimation can be order-optimal without interaction.
problem Can 1-bit mean estimation be optimal without interaction?
method Adaptive and non-adaptive threshold and interval queries, with one adaptive transition.
result Arbitrary non-adaptive quantizers can match the adaptive rate, suggesting interaction is not necessary.
A new framework RTK accelerates diffusion inference by breaking down the process into fewer, more efficient subproblems.
problem Efficiently generating data from trained diffusion models using discretized reverse SDEs or ODEs.
method Developed a general RTK framework that decomposes the diffusion process into fewer, more balanced subproblems, using MALA and ULD for sampling.
result The RTK-MALA and RTK-ULD algorithms achieve faster convergence rates and lower error compared to existing methods.
Proposes a method for approximating transition densities of SDEs driven by gamma processes.
problem Calculating transition densities for SDEs driven by gamma processes.
method Taylor-type approximation and conditional expectation of multiple stochastic integrals.
result Efficiency of the proposed method demonstrated through numerical tests.
Diffusion models reveal latent hierarchical structure in data.
problem Quantitative measurement of data's hierarchical structure.
method Forward-backward experiments in diffusion models.
result Changes in latent variables manifest as correlated chunks in data.
Generative diffusion models are analyzed for their information dynamics.
problem Lack of a unified theoretical understanding of generative diffusion models.
method Integrated perspective connecting information-theoretic, dynamical, and thermodynamic aspects.
result Generative bandwidth is directly governed by the divergence of the score function's vector field.
We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existen…
Develops methods to simulate rare transitions in molecular systems.
problem Rare transitions between metastable states in molecular systems are difficult to study due to limited data.
method Two novel methods: chain-based and midpoint-based approaches.
result Demonstrates effectiveness of methods in both data-rich and data-scarce scenarios.
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
The study uncovers the conditions under which diffusion models memorize or generalize.
problem Understanding the balance between memorization and generalization in diffusion models.
method Theoretical and mathematical framework to investigate memorization and generalization in diffusion models.
result Theoretical crossover point predicts a phase transition in diffusion models, validating the hypothesis.
A new method for sampling from posterior distributions in Bayesian inverse problems.
problem Sampling from posterior distributions in Bayesian inverse problems is challenging due to intractable terms.
method Proposes a novel approach that decomposes the transitions, allowing a trade-off between complexity of guidance term and prior transitions.
result Validated through experiments on various inverse problems, including challenging cases with latent diffusion models as priors.
The paper analyzes reflected diffusion models on hypercube data.
problem Challenges in modeling bounded domains with low-dimensional data.
method Employed an infinite series expansion of transition densities to bound the score function and its approximation.
result Established convergence rates for generative algorithm adapting to intrinsic dimensionality.
AdaCAD improves semi-supervised classification by focusing on intra-class nodes.
problem Improving semi-supervised classification by addressing inter-class connections in graphs.
method AdaCAD uses a class-attentive diffusion process to adaptively aggregate nodes based on their class similarity.
result AdaCAD significantly outperforms state-of-the-art methods in semi-supervised classification.
We present new extensions to a method for constructing several families of solvable one-dimensional time-homogeneous diffusions whose transition densities are obtainable in analytically closed-form. Our approach is based on a dual application of the so-called diffusion canonical transformation method that combines smoo…
We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The sym…
In this paper mechanisms of reversion - momentum transition are considered. Two basic nonlinear mechanisms are highlighted: a slow and fast bifurcation. A slow bifurcation leads to the equilibrium evolution, preceded by stability loss delay of a control parameter. A single order parameter is introduced by Markovian cha…
We consider a structural model where the survival/default state is observed together with a noisy version of the firm value process. This assumption makes the model more realistic than most of the existing alternatives, but triggers important challenges related to the computation of conditional default probabilities. I…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is studied as an example of bundle-like objects with discordant (sogo) transition functi…