diff --git a/intro.md b/intro.md
index 57bd80c..08b950c 100644
--- a/intro.md
+++ b/intro.md
@@ -15,7 +15,7 @@ We are living in an era of rapid transformation. These methods have the potentia
 
 ```{note} 
 _What's new in v0.3?_
-This latest edition takes things even further with a major new chapter on generative modeling, covering cutting-edge techniques like denoising, flow-matching, autoregressive learning, physics-integrated constraints, and diffusion-based graph networks. We've also introduced a dedicated section on neural architectures specifically designed for physics simulations. All code examples have been updated to leverage the latest frameworks.
+This latest edition adds a major new chapter on generative modeling, covering powerful techniques like denoising, flow-matching, autoregressive learning, physics-integrated constraints, and diffusion-based graph networks. We've also introduced a dedicated section on neural architectures specifically designed for physics simulations. All code examples have been updated to leverage the latest frameworks.
 ```
 
 ---
diff --git a/overview-optconv.md b/overview-optconv.md
index ba51031..27ee3fc 100644
--- a/overview-optconv.md
+++ b/overview-optconv.md
@@ -62,7 +62,7 @@ In several instances we'll make use of the fundamental theorem of calculus, repe
 $$f(x+\Delta) = f(x) + \int_0^1 \text{d}s ~ f'(x+s \Delta) \Delta \ . $$
 
 In addition, we'll make use of Lipschitz-continuity with constant $\mathcal L$:
-$|f(x+\Delta) + f(x)|\le \mathcal L \Delta$, and the well-known Cauchy-Schwartz inequality: 
+$|f(x+\Delta) - f(x)|\le \mathcal L \Delta$, and the well-known Cauchy-Schwartz inequality: 
 $ u^T v \le |u| \cdot |v| $.
 
 ## Newton's method
diff --git a/probmodels-diffusion.ipynb b/probmodels-diffusion.ipynb
index 91f9a99..a4c3314 100644
--- a/probmodels-diffusion.ipynb
+++ b/probmodels-diffusion.ipynb
@@ -31,7 +31,7 @@
         "Given a data point $x_0$, we can sample the noisy latent state $x_t$ from the forward Markov chain via\n",
         "\n",
         "$$\n",
-        "    q(x_t|x_0) = \\mathcal{N}(x_t, \\sqrt{\\overline{\\alpha}_t}x_0, (1-\\overline{\\alpha}_t)I)) ,\n",
+        "    q(x_t|x_0) = \\mathcal{N}(\\sqrt{\\overline{\\alpha}_t}x_0, (1-\\overline{\\alpha}_t)I)) ,\n",
         "$$\n",
         "\n",
         "with the inverted weights $\\alpha_t = 1 - \\beta_t$ and alphas accumulated for time $t$ denoted by\n",
diff --git a/references.bib b/references.bib
index c13d128..61643f4 100644
--- a/references.bib
+++ b/references.bib
@@ -13,6 +13,14 @@
 @STRING{NeurIPS        = "Advances in Neural Information Processing Systems"}
 
 
+@article{braun2025msbg,
+  title  ={{Adaptive Phase-Field-FLIP for Very Large Scale Two-Phase Fluid Simulation}},
+  author = {Braun, Bernhard and Bender, Jan and Thuerey, Nils},
+  journal = {{ACM} Transaction on Graphics},
+  volume = {44 (3)},
+  year = {2025},
+  publisher = {ACM},
+} 
 
 @inproceedings{lino2025dgn,
   title={Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks},