The Score Field: How Diffusion Models Find the Data
A diffusion model learns the score, the arrows that point towards more likely data at every noise level. Start from pure noise, follow the arrows while the noise fades, and you land on the data. Real trained network, real sampling.
- A small score network s(x, σ) ≈ ∇log p_σ(x), trained by denoising score matching on a spiral
- High noise (σ = 1.2): every arrow points broadly to the centre
- Low noise (σ = 0.02): the arrows hug the spiral
- Learned vs exact score: cosine 0.97 at σ = 0.1, 1.00 at σ = 1.0
- 2,000 samples of pure noise follow the probability-flow ODE dx = −σ ∇log p_σ dσ (300 Heun steps)
- Mean distance to the nearest training point: 0.42 → 0.012 (real held-out data: 0.011)
- The surface is the noised data density p_σ, sharpening as σ falls
- Diffusion = follow the score while the noise fades
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#shorts #diffusionmodels #scorematching #generativeai #deeplearning #machinelearning #3d #stablediffusion #cheatsheet #ai #datascience #python #coding #programming #tech #learnai
A diffusion model learns the score, the arrows that point towards more likely data at every noise level. Start from pure noise, follow the arrows while the noise fades, and you land on the data. Real trained network, real sampling.
- A small score network s(x, σ) ≈ ∇log p_σ(x), trained by denoising score matching on a spiral
- High noise (σ = 1.2): every arrow points broadly to the centre
- Low noise (σ = 0.02): the arrows hug the spiral
- Learned vs exact score: cosine 0.97 at σ = 0.1, 1.00 at σ = 1.0
- 2,000 samples of pure noise follow the probability-flow ODE dx = −σ ∇log p_σ dσ (300 Heun steps)
- Mean distance to the nearest training point: 0.42 → 0.012 (real held-out data: 0.011)
- The surface is the noised data density p_σ, sharpening as σ falls
- Diffusion = follow the score while the noise fades
Save it, share it with a friend who is learning AI, and pause the video to read every detail.
Subscribe for more: https://www.youtube.com/@mehdihosseinimoghadam
GitHub: https://github.com/mehdihosseinimoghadam
LinkedIn: https://linkedin.com/in/mehdi-hosseini-moghadam-384912198
#shorts #diffusionmodels #scorematching #generativeai #deeplearning #machinelearning #3d #stablediffusion #cheatsheet #ai #datascience #python #coding #programming #tech #learnai
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