DistillKac: Few-Step Image Generation via Damped Wave Equations

• URL: http://arxiv.org/abs/2509.21513v1
• Date: Thu, 25 Sep 2025 20:04:41 GMT
• Title: DistillKac: Few-Step Image Generation via Damped Wave Equations
• Authors: Weiqiao Han, Chenlin Meng, Christopher D. Manning, Stefano Ermon,
• Abstract summary: We present DistillKac, a fast image generator that uses the damped wave equation and its Kac representation to move probability mass at finite speed.<n>In contrast to diffusion models whose reverse time velocities can become stiff and implicitly allow unbounded propagation speed, Kac dynamics enforce finite speed transport and yield globally bounded kinetic energy.
• Score: 83.5291918320052
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present DistillKac, a fast image generator that uses the damped wave equation and its stochastic Kac representation to move probability mass at finite speed. In contrast to diffusion models whose reverse time velocities can become stiff and implicitly allow unbounded propagation speed, Kac dynamics enforce finite speed transport and yield globally bounded kinetic energy. Building on this structure, we introduce classifier-free guidance in velocity space that preserves square integrability under mild conditions. We then propose endpoint only distillation that trains a student to match a frozen teacher over long intervals. We prove a stability result that promotes supervision at the endpoints to closeness along the entire path. Experiments demonstrate DistillKac delivers high quality samples with very few function evaluations while retaining the numerical stability benefits of finite speed probability flows.

Related papers

• IDLM: Inverse-distilled Diffusion Language Models [70.5793829229702]
  We extend Inverse Distillation, a technique originally developed to accelerate continuous diffusion models, to the discrete setting.<n>From a theoretical perspective, the inverse distillation objective lacks uniqueness guarantees, which may lead to suboptimal solutions.<n>We show that our method, Inverse-distilled Diffusion Language Models (IDLM), reduces the number of inference steps by 4x-64x.
  arXiv  Detail & Related papers  (2026-02-22T06:47:04Z)
• A Kinetic-Energy Perspective of Flow Matching [23.42786172624299]
  Flow-based generative models can be viewed through a physics lens.<n>Motivated by classical mechanics, we introduce Kinetic Path Energy (KPE)<n>We show that extreme energies drive trajectories toward near-copies of training examples.
  arXiv  Detail & Related papers  (2026-02-08T11:51:50Z)
• Instantaneous velocity during quantum tunnelling [16.3770639786505]
  Quantum tunnelling allows particles to pass through the classically forbidden region.<n>We show that the particle velocity inside the barrier relaxes from a large initial value toward a smaller one, and may even approach zero.<n>We point out that defining an effective speed from the probability density, rather than from the probability current, can lead to spuriously nonzero "stationary speed"
  arXiv  Detail & Related papers  (2025-12-18T10:28:38Z)
• Fast momentum-selective transport of Bose-Einstein condensates via controlled non-adiabatic dynamics in optical lattices [0.0]
  We study a protocol for momentum-selective transport of a Bose-Einstein condensate (BEC) in a one-dimensional optical lattice.<n>We identify the intra-site breathing dynamics as the dominant mechanism governing spectral purity under fast loading conditions.<n>This approach is particularly relevant for quantum sensors operating under stringent timing constraints.
  arXiv  Detail & Related papers  (2025-09-19T19:15:44Z)
• Telegrapher's Generative Model via Kac Flows [1.2499537119440245]
  We propose a new flow-based generative model based on the damped wave equation, also known as telegrapher's equation.<n>Using the framework of flow matching, we train a neural network that approximates the velocity field and use it for sample generation.
  arXiv  Detail & Related papers  (2025-06-25T17:37:21Z)
• Computational Stochastic Mechanics of a Simple Bound State [0.0]
  We calculate probability density distributions using concepts of mechanics independent of bootstrapping with a known wave function.<n>We explore the effect of energy defect off of the ground state energy on the velocity field, which dictates how a particle interacts with the background of fluctuations in position.
  arXiv  Detail & Related papers  (2025-04-11T16:22:23Z)
• Trajectory Consistency Distillation: Improved Latent Consistency Distillation by Semi-Linear Consistency Function with Trajectory Mapping [75.72212215739746]
  Trajectory Consistency Distillation (TCD) encompasses trajectory consistency function and strategic sampling. TCD significantly enhances image quality at low NFEs but also yields more detailed results compared to the teacher model.
  arXiv  Detail & Related papers  (2024-02-29T13:44:14Z)
• DiffuSeq-v2: Bridging Discrete and Continuous Text Spaces for Accelerated Seq2Seq Diffusion Models [58.450152413700586]
  We introduce a soft absorbing state that facilitates the diffusion model in learning to reconstruct discrete mutations based on the underlying Gaussian space. We employ state-of-the-art ODE solvers within the continuous space to expedite the sampling process. Our proposed method effectively accelerates the training convergence by 4x and generates samples of similar quality 800x faster.
  arXiv  Detail & Related papers  (2023-10-09T15:29:10Z)
• Self-Consistent Velocity Matching of Probability Flows [22.2542921090435]
  We present a discretization-free scalable framework for solving a class of partial differential equations (PDEs) The main observation is that the time-varying velocity field of the PDE solution needs to be self-consistent. We use an iterative formulation with a biased gradient estimator that bypasses significant computational obstacles with strong empirical performance.
  arXiv  Detail & Related papers  (2023-01-31T16:17:18Z)
• Self-Consistency of the Fokker-Planck Equation [117.17004717792344]
  The Fokker-Planck equation governs the density evolution of the Ito process. Ground-truth velocity field can be shown to be the solution of a fixed-point equation. In this paper, we exploit this concept to design a potential function of the hypothesis velocity fields.
  arXiv  Detail & Related papers  (2022-06-02T03:44:23Z)
• Hessian-Free High-Resolution Nesterov Acceleration for Sampling [55.498092486970364]
  Nesterov's Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed. This work explores the sampling counterpart of this phenonemon and proposes a diffusion process, whose discretizations can yield accelerated gradient-based MCMC methods.
  arXiv  Detail & Related papers  (2020-06-16T15:07:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.