Merge pull request #67 from standardAI/patch-2

Update 02_diffusion_models_from_scratch.ipynb

Author: johnowhitaker

unit1/02_diffusion_models_from_scratch.ipynb

@@ -425,7 +425,7 @@
     "id": "HafjRb3Md655"
    },
    "source": [
-    "As noise amount approaches one, our data begins to look like pure random noise. But for most noie_amounts, you can guess the digit fairly well. Do you think this is optimal?"
+    "As noise amount approaches one, our data begins to look like pure random noise. But for most noise amounts, you can guess the digit fairly well. Do you think this is optimal?"
    ]
   },
   {
@@ -1484,7 +1484,7 @@
     "q(\\mathbf{x}_{1:T} \\vert \\mathbf{x}_0) = \\prod^T_{t=1} q(\\mathbf{x}_t \\vert \\mathbf{x}_{t-1})$<br><br>\n",
     "\n",
     "\n",
-    "That is, we take $x_{t-1}$, scale it by $\\sqrt{1 - \\beta_t}$ and add noise scaled by $\\beta_t$. This $\\beta$ is defined for every t accoridng to some schedule, and determines how much noise is added per timestep. Now, we don't necessariy want to do this operation 500 times to get $x_{500}$ so we have another formula to get $x_t$ for any t given $x_0$: <br><br>\n",
+    "That is, we take $x_{t-1}$, scale it by $\\sqrt{1 - \\beta_t}$ and add noise scaled by $\\beta_t$. This $\\beta$ is defined for every t according to some schedule, and determines how much noise is added per timestep. Now, we don't necessarily want to do this operation 500 times to get $x_{500}$ so we have another formula to get $x_t$ for any t given $x_0$: <br><br>\n",
     "\n",
     "$\\begin{aligned}\n",
     "q(\\mathbf{x}_t \\vert \\mathbf{x}_0) &= \\mathcal{N}(\\mathbf{x}_t; \\sqrt{\\bar{\\alpha}_t} \\mathbf{x}_0, \\sqrt{(1 - \\bar{\\alpha}_t)} \\mathbf{I})\n",
@@ -1667,10 +1667,10 @@
     "\n",
     "Exactly how we take these steps depends on the sampling method used. We won't go into the theory too deeply, but some key design questions are:\n",
     "- How large of a step should you take? In other words, what 'noise schedule' should you follow?\n",
-    "- Do you use only the model's current prediction to inform the update step (like DDPM, DDIM and many others)? Do you evaluate the model several times to estimate higher-order gradients for a larger, more accurate step (higher order methods and some discrete ODE solvers)? Or do you keep a history of past predictions to try and better inform the current update step (linear multi-step and ancestral samplers). \n",
+    "- Do you use only the model's current prediction to inform the update step (like DDPM, DDIM and many others)? Do you evaluate the model several times to estimate higher-order gradients for a larger, more accurate step (higher-order methods and some discrete ODE solvers)? Or do you keep a history of past predictions to try and better inform the current update step (linear multi-step and ancestral samplers)? \n",
     "- Do you add in additional noise (sometimes called churn) to add more stochasticity (randomness) to the sampling process, or do you keep it completely deterministic? Many samplers control this with a parameter (such as 'eta' for DDIM samplers) so that the user can choose.\n",
     "\n",
-    "Research on sampling methods for diffusion models is rapidly evolving, and more and more methods for finding good solutions in fewer steps are being proposed. The brave and curious might find it interesting to browse through the code of the different implementations available in the diffusers library [here](https://github.com/huggingface/diffusers/tree/main/src/diffusers/schedulers) or check out the [docs](https://huggingface.co/docs/diffusers/api/schedulers) which often link to the relevant papers."
+    "Research on sampling methods for diffusion models is rapidly evolving, and more and more methods for finding good solutions in fewer steps are being proposed. The brave and curious might find it interesting to browse through the code of the different implementations available in the diffusers library [here](https://github.com/huggingface/diffusers/tree/main/src/diffusers/schedulers) or check out the [docs](https://huggingface.co/docs/diffusers/api/schedulers/overview) which often link to the relevant papers."
    ]
   },
   {