Diffusion Models

We can consider a model between random noise and trees.

For every step, we sample Gaussian noise and add it to the image. The original approach adds Gaussian to the pixels, and nowadays people replace the pixel.

Usually, there is a few thousand steps of noising.

Why is it that we can’t have a one-step policy from noise to pictures? Because of a physics result that says the stability of diffusion becomes intractable at too large steps.

• standard normal density function, and formula for phi for ARBITURARY normals (x-u/sigma)
  • practice using inverse phi
• BEWARE that sigma is not sigma squared
• PDF AND CDF, Mean, Var, params, Generative Story for:
  • uniform distribution and the normal distribution
  • all of these
• continuity correction
• permutation and combinations formula
• counting formulas: binning, stars and bars, and the counting methods tree from beginning of class
• probability theorems: law of total probabaly, baysian, demorgans, counting with and and or
• multinomial distribution
• binomial coefficient (i.e. combinations formula), multinomial coefficient
• joint probability distribution and their table
• Naive Bayes divison ratio trick
• relative probability

What if you don’t know about a probability of success?

Beta Distribution time!!!

Multi-Arm Bandit

See Multi-Arm Bandit

Strategies:

• upper confidence bound: take the action with theh highest n-tn-thonfidence bound
• Posterior Sampling: take a sample from each Beta Distributions distribution; take the action that has a higher probability of success based on their r

Key Sequence

Notation

New Concepts

• IID
• Zero-Sum Game
• central limit theorem
• bootstrap

Important Results / Claims

• Sum of Two Dice
• adding random variables

Questions

Interesting Factoids