Aircraft Traffic Control: Managing Order in a Crowded Sky
Published:
How Air Traffic Control keeps order in a crowded sky: separation, sequencing, and flow management viewed as a predictive, safety-critical control system.
Posts by Tags
ATC
Airspace
Aircraft Traffic Control: Managing Order in a Crowded Sky
Published:
How Air Traffic Control keeps order in a crowded sky: separation, sequencing, and flow management viewed as a predictive, safety-critical control system.
Algorithms
Algorithms for Decision-Making: From Uncertainty to Action
Published:
An overview of algorithms for decision-making under uncertainty — from probabilistic reasoning to MDPs and POMDPs — bridging theory and practice.
Autonomy
Algorithms for Decision-Making: From Uncertainty to Action
Published:
An overview of algorithms for decision-making under uncertainty — from probabilistic reasoning to MDPs and POMDPs — bridging theory and practice.
Aircraft Traffic Control: Managing Order in a Crowded Sky
Published:
How Air Traffic Control keeps order in a crowded sky: separation, sequencing, and flow management viewed as a predictive, safety-critical control system.
Decision-Making
Algorithms for Decision-Making: From Uncertainty to Action
Published:
An overview of algorithms for decision-making under uncertainty — from probabilistic reasoning to MDPs and POMDPs — bridging theory and practice.
Safety
Aircraft Traffic Control: Managing Order in a Crowded Sky
Published:
How Air Traffic Control keeps order in a crowded sky: separation, sequencing, and flow management viewed as a predictive, safety-critical control system.
Uncertainty
Algorithms for Decision-Making: From Uncertainty to Action
Published:
An overview of algorithms for decision-making under uncertainty — from probabilistic reasoning to MDPs and POMDPs — bridging theory and practice.
aerodynamics-performance
Aircraft Dynamics and Simulation From Scratch
Published:
Building an aircraft dynamics simulator from first principles — equations of motion, aerodynamic forces, stability, and performance, implemented step by step.
air-traffic-control
Fluid Dynamics Meets Air Traffic Control: A Novel Approach to Conflict Resolution
Published:
A novel take on conflict resolution that borrows from fluid dynamics — treating air traffic as a flow field to reason about separation assurance and deconfliction.
aircraft-dynamics
Aircraft Dynamics and Simulation From Scratch
Published:
Building an aircraft dynamics simulator from first principles — equations of motion, aerodynamic forces, stability, and performance, implemented step by step.
architectures
Architectures & Latent Diffusion
Published:
Time embeddings, U-Nets and Diffusion Transformers, and why moving to a VAE latent space made high-resolution generation practical.
bayes
Conditioning, Joints & Marginals
Published:
How distributions combine and decompose: joint densities, conditioning (slicing) and marginalizing (averaging) — the grammar of probabilistic models.
change-of-variables
Change of Variables & the Score
Published:
Transforming densities (the Jacobian and pushforwards) and a first, geometric look at the score gradient of log-density — the compass diffusion follows.
cnf
From CNFs to Flow Matching
Published:
Continuous normalizing flows and the likelihood bottleneck, then the flow-matching idea: just regress a velocity field.
conditioning
Conditioning & Classifier-Free Guidance
Published:
Conditioning on prompts and labels and the classifier-free guidance trick — plus the quality-vs-diversity trade-off you can dial.
conflict-resolution
Fluid Dynamics Meets Air Traffic Control: A Novel Approach to Conflict Resolution
Published:
A novel take on conflict resolution that borrows from fluid dynamics — treating air traffic as a flow field to reason about separation assurance and deconfliction.
ddim
The Probability-Flow ODE & Fast Samplers
Published:
The deterministic ODE with the same marginals as the SDE — DDIM, sampler choices, and the step-count vs quality trade-off.
ddpm
Learning to Denoise: the DDPM Objective
Published:
The reverse Gaussian, predicting the noise epsilon, and the simplified training loss — why a denoiser is all you need, from scratch.
The Forward Process & Noise Schedules
Published:
The Gaussian Markov chain, the closed-form forward marginal, and how the noise schedule controls how fast structure is destroyed.
Sampling: Your First Generations
Published:
Ancestral sampling from noise to data, your first generated samples on 2-D toys (and MNIST), and what the reverse trajectory looks like.
diffusion
Diffusion from First Principles: From Data to Noise and Back
Published:
The one idea behind every diffusion model — gradually destroy structure with noise, then learn to undo it — with an interactive forward-diffusion explorable to build intuition.
Score Matching
Published:
Denoising score matching and Tweedie’s formula — why predicting noise is the same as estimating the score, with a visual of the learned score field.
Numerics, Evaluation & Failure Modes
Published:
Samplers, EMA, numerical stability, and how we actually measure generative models (FID, likelihood) — plus the failure modes to watch for.
Learning to Denoise: the DDPM Objective
Published:
The reverse Gaussian, predicting the noise epsilon, and the simplified training loss — why a denoiser is all you need, from scratch.
The Forward Process & Noise Schedules
Published:
The Gaussian Markov chain, the closed-form forward marginal, and how the noise schedule controls how fast structure is destroyed.
Sampling: Your First Generations
Published:
Ancestral sampling from noise to data, your first generated samples on 2-D toys (and MNIST), and what the reverse trajectory looks like.
Conditioning & Classifier-Free Guidance
Published:
Conditioning on prompts and labels and the classifier-free guidance trick — plus the quality-vs-diversity trade-off you can dial.
From Markov Chains to SDEs
Published:
The forward VP/VE SDE, Anderson’s reverse-time SDE, and how DDPM is just a discretization of a continuous process.
discrete-diffusion
Discrete Diffusion & Scientific Applications
Published:
Diffusion beyond pixels: continuous-time Markov chains for language, and diffusion for molecules and protein structure.
dynamics
A Little Dynamics: ODEs, SDEs & Flows
Published:
Velocity fields and Euler integration, then an SDE is an ODE plus noise — the minimal dynamics needed to flow a density from noise to data.
evaluation
Numerics, Evaluation & Failure Modes
Published:
Samplers, EMA, numerical stability, and how we actually measure generative models (FID, likelihood) — plus the failure modes to watch for.
first-principles
Diffusion from First Principles: From Data to Noise and Back
Published:
The one idea behind every diffusion model — gradually destroy structure with noise, then learn to undo it — with an interactive forward-diffusion explorable to build intuition.
flow-matching
Diffusion as a Special Case; Rectified Flows
Published:
Recovering diffusion from the flow-matching lens, and straightening paths (rectified flow / OT) for faster, cleaner sampling.
Conditional Flow Matching
Published:
Conditional probability paths and vector fields, and the marginalization trick that makes flow matching trainable without simulating the flow.
From CNFs to Flow Matching
Published:
Continuous normalizing flows and the likelihood bottleneck, then the flow-matching idea: just regress a velocity field.
fluid-dynamics
Fluid Dynamics Meets Air Traffic Control: A Novel Approach to Conflict Resolution
Published:
A novel take on conflict resolution that borrows from fluid dynamics — treating air traffic as a flow field to reason about separation assurance and deconfliction.
fokker-planck
From Markov Chains to SDEs
Published:
The forward VP/VE SDE, Anderson’s reverse-time SDE, and how DDPM is just a discretization of a continuous process.
foundations
Probability You Can See: Densities, Sampling & Expectation
Published:
Random variables, densities, and the idea that an expectation is just an average over samples — the Monte-Carlo lens we use everywhere.
Conditioning, Joints & Marginals
Published:
How distributions combine and decompose: joint densities, conditioning (slicing) and marginalizing (averaging) — the grammar of probabilistic models.
gaussian
Gaussians & the Reparameterization Trick
Published:
The Gaussian is the workhorse of generative modeling. Here’s everything you need — mean, covariance, and the one trick (x = μ + σε) that makes diffusion trainable.
generative-ai
Gaussians & the Reparameterization Trick
Published:
The Gaussian is the workhorse of generative modeling. Here’s everything you need — mean, covariance, and the one trick (x = μ + σε) that makes diffusion trainable.
Diffusion from First Principles: From Data to Noise and Back
Published:
The one idea behind every diffusion model — gradually destroy structure with noise, then learn to undo it — with an interactive forward-diffusion explorable to build intuition.
From CNFs to Flow Matching
Published:
Continuous normalizing flows and the likelihood bottleneck, then the flow-matching idea: just regress a velocity field.
guidance
Conditioning & Classifier-Free Guidance
Published:
Conditioning on prompts and labels and the classifier-free guidance trick — plus the quality-vs-diversity trade-off you can dial.
information-theory
Measuring Distance Between Distributions: Likelihood & KL
Published:
Likelihood, cross-entropy, and KL divergence — why fitting a distribution means minimizing KL, and what that buys us.
kl-divergence
Measuring Distance Between Distributions: Likelihood & KL
Published:
Likelihood, cross-entropy, and KL divergence — why fitting a distribution means minimizing KL, and what that buys us.
language
Discrete Diffusion & Scientific Applications
Published:
Diffusion beyond pixels: continuous-time Markov chains for language, and diffusion for molecules and protein structure.
latent-diffusion
Architectures & Latent Diffusion
Published:
Time embeddings, U-Nets and Diffusion Transformers, and why moving to a VAE latent space made high-resolution generation practical.
monte-carlo
Probability You Can See: Densities, Sampling & Expectation
Published:
Random variables, densities, and the idea that an expectation is just an average over samples — the Monte-Carlo lens we use everywhere.
noise-schedule
The Forward Process & Noise Schedules
Published:
The Gaussian Markov chain, the closed-form forward marginal, and how the noise schedule controls how fast structure is destroyed.
numerics
Numerics, Evaluation & Failure Modes
Published:
Samplers, EMA, numerical stability, and how we actually measure generative models (FID, likelihood) — plus the failure modes to watch for.
ode
The Probability-Flow ODE & Fast Samplers
Published:
The deterministic ODE with the same marginals as the SDE — DDIM, sampler choices, and the step-count vs quality trade-off.
odes
A Little Dynamics: ODEs, SDEs & Flows
Published:
Velocity fields and Euler integration, then an SDE is an ODE plus noise — the minimal dynamics needed to flow a density from noise to data.
optimal-transport
Diffusion as a Special Case; Rectified Flows
Published:
Recovering diffusion from the flow-matching lens, and straightening paths (rectified flow / OT) for faster, cleaner sampling.
Conditional Flow Matching
Published:
Conditional probability paths and vector fields, and the marginalization trick that makes flow matching trainable without simulating the flow.
probability
Gaussians & the Reparameterization Trick
Published:
The Gaussian is the workhorse of generative modeling. Here’s everything you need — mean, covariance, and the one trick (x = μ + σε) that makes diffusion trainable.
Probability You Can See: Densities, Sampling & Expectation
Published:
Random variables, densities, and the idea that an expectation is just an average over samples — the Monte-Carlo lens we use everywhere.
Measuring Distance Between Distributions: Likelihood & KL
Published:
Likelihood, cross-entropy, and KL divergence — why fitting a distribution means minimizing KL, and what that buys us.
Conditioning, Joints & Marginals
Published:
How distributions combine and decompose: joint densities, conditioning (slicing) and marginalizing (averaging) — the grammar of probabilistic models.
Change of Variables & the Score
Published:
Transforming densities (the Jacobian and pushforwards) and a first, geometric look at the score gradient of log-density — the compass diffusion follows.
rectified-flow
Diffusion as a Special Case; Rectified Flows
Published:
Recovering diffusion from the flow-matching lens, and straightening paths (rectified flow / OT) for faster, cleaner sampling.
reparameterization
Gaussians & the Reparameterization Trick
Published:
The Gaussian is the workhorse of generative modeling. Here’s everything you need — mean, covariance, and the one trick (x = μ + σε) that makes diffusion trainable.
sampling
The Probability-Flow ODE & Fast Samplers
Published:
The deterministic ODE with the same marginals as the SDE — DDIM, sampler choices, and the step-count vs quality trade-off.
Sampling: Your First Generations
Published:
Ancestral sampling from noise to data, your first generated samples on 2-D toys (and MNIST), and what the reverse trajectory looks like.
science
Discrete Diffusion & Scientific Applications
Published:
Diffusion beyond pixels: continuous-time Markov chains for language, and diffusion for molecules and protein structure.
score
Change of Variables & the Score
Published:
Transforming densities (the Jacobian and pushforwards) and a first, geometric look at the score gradient of log-density — the compass diffusion follows.
score-matching
Diffusion from First Principles: From Data to Noise and Back
Published:
The one idea behind every diffusion model — gradually destroy structure with noise, then learn to undo it — with an interactive forward-diffusion explorable to build intuition.
Score Matching
Published:
Denoising score matching and Tweedie’s formula — why predicting noise is the same as estimating the score, with a visual of the learned score field.
sde
Score Matching
Published:
Denoising score matching and Tweedie’s formula — why predicting noise is the same as estimating the score, with a visual of the learned score field.
The Probability-Flow ODE & Fast Samplers
Published:
The deterministic ODE with the same marginals as the SDE — DDIM, sampler choices, and the step-count vs quality trade-off.
From Markov Chains to SDEs
Published:
The forward VP/VE SDE, Anderson’s reverse-time SDE, and how DDPM is just a discretization of a continuous process.
sdes
A Little Dynamics: ODEs, SDEs & Flows
Published:
Velocity fields and Euler integration, then an SDE is an ODE plus noise — the minimal dynamics needed to flow a density from noise to data.
separation-assurance
Fluid Dynamics Meets Air Traffic Control: A Novel Approach to Conflict Resolution
Published:
A novel take on conflict resolution that borrows from fluid dynamics — treating air traffic as a flow field to reason about separation assurance and deconfliction.
simulation
Aircraft Dynamics and Simulation From Scratch
Published:
Building an aircraft dynamics simulator from first principles — equations of motion, aerodynamic forces, stability, and performance, implemented step by step.
stability
Aircraft Dynamics and Simulation From Scratch
Published:
Building an aircraft dynamics simulator from first principles — equations of motion, aerodynamic forces, stability, and performance, implemented step by step.
training
Learning to Denoise: the DDPM Objective
Published:
The reverse Gaussian, predicting the noise epsilon, and the simplified training loss — why a denoiser is all you need, from scratch.
vae
Architectures & Latent Diffusion
Published:
Time embeddings, U-Nets and Diffusion Transformers, and why moving to a VAE latent space made high-resolution generation practical.