empirical data flowing
to emergent geometry.

Generative and geometric machine learning — developed rigorously, deployed at scale, for scientific discovery.

Mission

The boundary between mathematics, physics, and machine learning is dissolving. Transformers, diffusion maps, and stochastic dynamics are not separate tools — they are different regimes of the same geometry.

DAC is built on this unification. We develop the infrastructure to run these methods at scales that matter to science.

Flagship · Private beta
FlashDiffusion

Coifman–Lafon diffusion maps at 100M-sample scale. B300-native sparse eigensolver. Hours, not weeks. Built for MD trajectories, cryo-EM, XFEL, and beyond.

1Mframes · 30 min
100Mmax samples
B300GPU native
Coming soon
More to come

Additional solutions in development.

All solutions →

Documentation is being written in parallel with the codebase. API reference, tutorials, and theory-to-code guides will ship here as the platform moves out of private beta.

Getting started
Quickstart Guide

Submit your first run. Dataset formats, parameter reference, and reading your results.

In progress
API Reference
Worker API

Endpoint schema, field definitions, response format, and error codes for the FlashDiffusion API.

In progress
Theory to code
DMAP in Practice

How Coifman–Lafon diffusion maps translate to the FlashDiffusion pipeline, step by step.

Coming soon

// In the meantime: arXiv 2604.09560 is the primary reference  ·  GitHub has the source

View documentation →
Λc = F − c ∧ c

The Diffusion–Attention Connection

Transformers, diffusion maps, and magnetic Laplacians are different regimes of a single Markov geometry built from query–key scores — unified through the static Schrödinger bridge framework. DMAP is the equilibrium sector. Attention is NESS. The same equation governs both.

Read the theory →
P⁺ = diag(Z)⁻¹P
Diffusion operator

Row-stochastic transition matrix. Encodes manifold geometry, not sampling density.

Λc = F − c ∧ c
Cartan's structure equation

F = 0 gives DMAP (equilibrium). F ≠ 0 gives attention (NESS).

Ψt = (λ₁ᵗψ₁, …, λₘᵗψₘ)
Diffusion coordinates

Eigenvector embedding weighted by eigenvalues. Euclidean distance = diffusion distance.