---
title: 【論文サーベイ】Stochastic Differential Equations and Diffusion Models
tags: 
author: [tf63](https://www.docswell.com/user/8590143908)
site: [Docswell](https://www.docswell.com/)
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description: 【論文サーベイ】Stochastic Differential Equations and Diffusion Models by tf63
published: October 25, 23
canonical: https://www.docswell.com/s/8590143908/Z4Q64Y-2023-10-25-145507
---
# Page. 1

![Page Image](https://bcdn.docswell.com/page/VJPXR3VL78.jpg)

Stochastic Differential Equations and Diffusion Model
Keyword
●
●
●
SDE: Stochastic Differential Equations
SDEdit
(inverse problem)
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Summary
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# Page. 3

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Stochastic Differential Equations and Diffusion Model
Score-Based Generative Modeling through SDEs, (Score SDE)
Y. Song, J. Sohl-Dickstein, D. P. Kingma, A.Kumar, S. Ermon, B. Poole [ICLR’21]
SDEdit: Guided Image Synthesis and Editing with SDEs, (SDEdit)
C.Meng, Y. He, Y. Song, J. Song, J. Wu, J. Zhu, S.Ermon [NeurIPS’21]
Diffusion Models for Adversarial Purification, (DiffPure)
W.Nie, B.Guo, Y.Huang , C.Xiao, A.Vahdat, A. Anandkumar [ICML’22]
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Background (1/3) Diffusion Model
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Background (2/3) 確率微分方程式 (SDE)
SDEは次式で与えられる
ウィーナー過程はあらゆる点で微
分不可能
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Background (3/3) 拡散モデルで扱うSDE
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![Page Image](https://bcdn.docswell.com/page/GEW3R1R3E2.jpg)

Score-Based Generative Modeling through SDEs, (Score SDE)
Y. Song, J. Sohl-Dickstein, D. P. Kingma, A.Kumar, S. Ermon, B. Poole [ICLR’21]
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連続化すると何が嬉しい ?
Flexible sampling and likelihood computation
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様々なSDE-solverを使うことができ，サンプリング効率を上げられる
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ODEに変換できる (後述)
Controllable Generation
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unconditionalなモデルに対して，scoreを使ってcondition可能
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classifier guidanceのような手法を用いてconditionを強くできる
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class-conditional generation, inverse problemに対して応用できる
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DDPMからSDEの導出 (Forward SDE)
DDPMのForward
と変換
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![Page Image](https://bcdn.docswell.com/page/GJ5Y8Z82J4.jpg)

DDPMからSDEの導出 (Forward SDE)
DDPMのForward SDE
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DDPMからSDEの導出 (Forward SDE)
SDEの形
DDPMのForward SDE
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DDPMからSDEの導出 (Reverse SDE)
導出
※証明は省略
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Euler-Maruyama法によるサンプリング
区間を再び離散化
Reverse SDE
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評価
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(余談) ODE化すると ?
Exact likelihood computation
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次式で対数尤度を正確に評価できる
Manipulating latent representations
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データ点
を潜在空間
に射影できる
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再構成を使って正確に画像編集ができる
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(余談) 実験結果
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SDEdit: Guided Image Synthesis and Editing with SDEs, (SDEdit)
C.Meng, Y. He, Y. Song, J. Song, J. Wu, J. Zhu, S.Ermon [NeurIPS’21]
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FaithfulとRealisticの間のトレードオフ
ノイズ
小
大
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先行手法: GAN inversion
Diffusion
GAN inversion
手の情報が消滅
DiffusionCLIP [G. Kim, 2022]
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評価
sample from stroke
stroke-based edit
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Diffusion Models for Adversarial Purification, (DiffPure)
W.Nie, B.Guo, Y.Huang , C.Xiao, A.Vahdat, A. Anandkumar [ICML’22]
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評価
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評価
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評価
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Summary
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