扩散模型完整数学

Layout

Three-row horizontal layout: Row 1 shows “前向过程 Forward” (x₀→x_T with noise increasing), Row 2 shows “反向过程 Reverse” (x_T→x₀ with denoising), Row 3 shows “CFG Classifier-Free Guidance” formula and intuition. A large central vertical arrow connects Row 1 and Row 2. Title “扩散模型” at top.

ZONES

Title Zone: Top center, “扩散模型 Diffusion” in large handwritten font with a star ★, small noise dots decoration
Row 1 - Forward Process: Left to right flow
- x₀ (clean image icon) → progressively noisier icons → x_T (pure noise icon)
- Key formula displayed prominently below the flow
- Show α_t, ᾱ_t notation
Row 2 - Reverse Process: Right to left flow (opposite direction)
- x_T (noise) → progressively cleaner icons → x₀ (clean)
- Loss function formula displayed prominently
- DDPM sampling algorithm in a small code-like box
- DDIM note as a side tag
Row 3 - CFG: Two parallel paths merging
- Left path: ε_unc (unconditional prediction)
- Right path: ε_cond (conditional prediction)
- Merging point: CFG formula with guidance scale s
- Visual: two arrows combining into one stronger arrow
Right Side Panel - 3D Advantages: Small vertical list of why diffusion beats GAN for 3D

LABELS

Forward Process: “前向加噪 Forward”, “q(x_t|x_{t-1}) = N(√α_t·x_{t-1}, β_t·I)”, “β_t: 10⁻⁴ → 0.02 线性调度”, “★核心公式: x_t = √ᾱ_t·x₀ + √(1-ᾱ_t)·ε”, “α_t = 1-β_t”, “ᾱ_t = ∏α_s”, “ε ~ N(0,I)”, “归纳法证明: 方差相加”
Reverse Process: “反向去噪 Reverse”, “L = E[‖ε - ε_θ(x_t, t)‖²]”, “预测噪声ε而非x₀ (优化landscape更平滑)”, “DDPM: x_{t-1} = (1/√α_t)(x_t - (1-α_t)/√(1-ᾱ_t)·ε) + √β_t·z”, “DDIM: 非马尔可夫 10~50步加速”
CFG: “Classifier-Free Guidance”, “ε̂ = ε_unc + s·(ε_cond - ε_unc)”, “s=1: 普通条件采样”, “s>1: 增强条件对齐牺牲多样性”, “10%概率丢弃条件(训练时)”
3D Panel: “3D优势”, “① MSE损失训练稳定”, “② 分数函数指向数据流形”, “③ CFG灵活条件化”, “④ 多尺度学习粗→细”

COLORS

Background: Warm Cream (#F5F0E8)
Forward row: very light Macaron Blue (#A8D8EA) background strip
Reverse row: very light Peach (#FFD5C2) background strip
CFG row: very light Lavender (#D5C6E0) background strip
Clean data icons (x₀): Macaron Blue (#A8D8EA) fill
Noisy data icons (x_T): grey with scattered dots
Central connecting arrow: Mustard Yellow (#F2CC8F)
Core formula box: Peach (#FFD5C2) border, large Coral Red (#E8655A) text
Loss function: Coral Red (#E8655A)
DDPM code box: Mint (#B5E5CF) background
CFG formula: Coral Red (#E8655A) in large font
ε_unc path: Lavender (#D5C6E0)
ε_cond path: Macaron Blue (#A8D8EA)
Merged arrow: Coral Red (#E8655A) bold
3D advantages panel: Mint (#B5E5CF) background with small checkmark icons

STYLE

Flat vector illustration. Clean black outlines on all elements. Progressive noise shown as icons going from clear geometric shapes to random scattered dots. Arrows are clean with arrowheads. Code-like box uses monospace-style font. Star ★ next to core formula. Small decorative noise patterns. No gradients. Keywords in bold handwritten-style font, formulas in clean sans-serif at large size.

ASPECT

3:4 portrait (tall format to accommodate three rows of content)

Clean composition with generous white space. Simple or no background. Main elements centered or positioned by content needs. Color values (#hex) and color names are rendering guidance only — do NOT display color names, hex codes, or palette labels as visible text in the image. Text should be large and prominent with handwritten-style fonts. Keep minimal, focus on keywords. Language: Chinese.