added diff-models graph section, intro probmodels-ddpm-fm

_toc.yml

@@ -39,6 +39,7 @@ parts:
   - file: probmodels-ddpm-fm.ipynb
   - file: probmodels-time.ipynb
   - file: probmodels-uncond.md
+  - file: probmodels-graph.md
 - caption: Reinforcement Learning
   chapters:
   - file: reinflearn-intro.md

probmodels-ddpm-fm.ipynb

@@ -8,9 +8,9 @@
    "source": [
     "# From DDPM to Flow Matching\n",
     "\n",
-    "Ever wondered how to turn your existing _denoising diffusion code_ into a _flow matching_ approach? 🤔 Or what all the fuss regarding diffusion models was about in the first place? 🧐 That's exactly what this notebook is focusing on 😎\n",
+    "We'll be using a learning task where we can reliably generate arbitrary amounts of ground truth data, to make sure 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",
     "\n",
-    "We'll be using a learning task where we can reliably generate arbitrary amounts of ground truth data, to make sure 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/).)\n",
+    "> Note, if you're directly continuing reading from the previous chapter: an important difference to {doc}`probmodels-intro` is that, for simplicity, we'll apply denoising and flow-matching to a _forward_ problem here! We won't be aiming to recover $x$ for an observation $y$, but rather assume we have initial conditions $x$ from which we want to compute a solution $y$. So don't be surprised by the switched $x$ and $y$ below.\n",
     "\n",
     "## Intro\n",
     "\n",