EDM: E(3) Equivariant Diffusion model

Equivariace를 만족하는 3D diffusion model (EDM)

▷ Introduction

분자의 분석과 합성에 관한 딥러닝 모델이 많음

기존의 3D 모델은 cost가 높음 (비효율적)

우리의 모델
1. atom coordinate & atom type 계산 가능 → categorical 어떻게 구현했는지
2. 첫 3D diffusion model → E3 equivariace 어떻게 구현했는지
3. 효율적

▷ Diffusion Models

>  Forward Process

denoising... 

SNR(t)

true denoising...

> Backward Process

> Training loss

Reconstruction loss

Regularization loss

Denoising process

DDPM 과 다른 부분

▷ Equivariance

Tg, Sg can be represented by a translation t and orthogonal matrix R (rotation, reflection)

 

> Equivariant Distributions and Diffusion...

equivariant of rotation and reflection

invariant of R transformations

invariant distribution에 equivariant function이 있어도 invariant distribution이 유지된다.

 

> Points and Features in E(3)...

h는 invariant

E(3) equivariant

> EGNNs

왼쪽이 본 논문, 오른쪽이 EGNN 논문

This transformation satisfies the required E(3) equivariant property.

 

▷ EDM: E(3) Equivariant Diffusion Model

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Algorithm of DDPM

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> Coordinates, Atom features

> Denoising process

True denoising process

equivariant function으로 입실론을 계산하므로, 이 식은 equivariant

> Training Loss

기존 diffusion model