Diffusion Models Explained

Difference between Ordinary differential equations (ODEs) and Stochastic differential equations (SDEs)

Ordinary differential equations (ODEs) describe deterministic systems where outcomes are fully determined by initial conditions and parameters - given the same starting point, you always get the same result. Stochastic differential equations (SDEs) incorporate random noise or uncertainty, making outcomes probabilistic rather than deterministic. For example, modeling a pendulum with an ODE gives a precise trajectory, while an SDE might include random forces like air turbulence. Stochastic processes are essential for modeling real-world phenomena with inherent randomness like stock prices, molecular motion, or population dynamics where uncertainty and random fluctuations play a crucial role in system behavior.

Some Links:

[Flow-Matching vs Diffusion Models explained side by side]

https://www.youtube.com/watch?v=firXjwZ_6KI

Comments

Simple Linear Regression - and Related Regression Loss Functions

Today's Topics: a. Regression Algorithms b. Outliers - Explained in Simple Terms c. Common Regression Metrics Explained d. Overfitting and Underfitting e. How are Linear and Non Linear Regression Algorithms used in Neural Networks [Future study topics] Regression Algorithms Regression algorithms are a category of machine learning methods used to predict a continuous numerical value. Linear regression is a simple, powerful, and interpretable algorithm for this type of problem. Quick Example: These are the scores of students vs. the hours they spent studying. Looking at this dataset of student scores and their corresponding study hours, can we determine what score someone might achieve after studying for a random number of hours? Example: From the graph, we can estimate that 4 hours of daily study would result in a score near 80. It is a simple example, but for more complex tasks the underlying concept will be similar. If you understand this graph, you will understand this blog. Sim...

What problems can AI Neural Networks solve

How does AI Neural Networks solve Problems? What problems can AI Neural Networks solve? Based on effectiveness and common usage, here's the ranking from best to least suitable for neural networks (Classification Problems, Regression Problems and Optimization Problems.) But first some Math, background and related topics as how the Neural Network Learn by training (Supervised Learning and Unsupervised Learning.) Background Note - Mathematical Precision vs. Practical AI Solutions. Math can solve all these problems with very accurate results. While Math can theoretically solve classification, regression, and optimization problems with perfect accuracy, such calculations often require impractical amounts of time—hours, days, or even years for complex real-world scenarios. In practice, we rarely need absolute precision; instead, we need actionable results quickly enough to make timely decisions. Neural networks excel at this trade-off, providing "good enough" solutions in seco...

Activation Functions in Neural Networks

A Guide to Activation Functions in Neural Networks 🧠 Question: Without activation function can a neural network with many layers be non-linear? Answer: Provided at the end of this document. Activation functions are a crucial component of neural networks. Their primary purpose is to introduce non-linearity , which allows the network to learn the complex, winding patterns found in real-world data. Without them, a neural network, no matter how deep, would just be a simple linear model. In the diagram below the f is the activation function that receives input and send output to next layers. Commonly used activation functions. 1. Sigmoid Function 2. Tanh (Hyperbolic Tangent) 3. ReLU (Rectified Linear Unit - Like an Electronic Diode) 4. Leaky ReLU & PReLU 5. ELU (Exponential Linear Unit) 6. Softmax 7. GELU, Swish, and SiLU 1. Sigmoid Function The classic "S-curve," Sigmoid squashes any input value t...

Artificial Intelligence Theory and Application

Search This Blog