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"id": "q4kVgOM2pyzJ"
},
"source": [
"# From DDPM to Flow Matching\n",
"# Denoising and Flow Matching Side-by-side\n",
"\n",
"To show the capabilities of **denoising diffusion** and **flow matching**, we'll be use a learning task where we can reliably generate arbitrary amounts of ground truth data. This ensures we can quantify how well the target distribution was learned. Specifically, we'll focus on Reynolds-averaged Navier-Stokes simulations around airfoils, which have the interesting characteristic that typical solvers (such as OpenFoam) transition from steady solutions to oscillating ones for larger Reynolds numbers. This transition is exactly what we'll give as a task to diffusion models below. (Details can be found in our [diffuion-based flow prediction repository](https://github.com/tum-pbs/Diffusion-based-Flow-Prediction/).) Also, to make the notebook self-contained, we'll revisit the most important concepts from the previous section.\n",
"[[run in colab]](https://colab.research.google.com/github/tum-pbs/pbdl-book/blob/main/probmodels-ddpm-fm.ipynb)\n",

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