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‎doc/pub/week13/html/week13-bs.html‎

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2,
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None,
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'diffusion-models-for-hierarchical-vae-from-url-https-arxiv-org-abs-2208-11970'),
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('Equation for the Markovian hierarchical VAE',
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2,
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None,
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'equation-for-the-markovian-hierarchical-vae'),
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('Variational Diffusion Models',
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2,
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None,
@@ -166,10 +162,6 @@
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('Encoder transitions', 2, None, 'encoder-transitions'),
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('Third assumption', 2, None, 'third-assumption'),
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('Noisification', 2, None, 'noisification'),
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('Diffusion models, from URL:"https://arxiv.org/abs/2208.11970"',
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2,
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None,
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'diffusion-models-from-url-https-arxiv-org-abs-2208-11970'),
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('Gaussian modeling', 2, None, 'gaussian-modeling'),
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('Optimizing the variational diffusion model',
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2,
@@ -270,14 +262,12 @@
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<!-- navigation toc: --> <li><a href="#mathematical-representation" style="font-size: 80%;">Mathematical representation</a></li>
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<!-- navigation toc: --> <li><a href="#back-to-the-marginal-probability" style="font-size: 80%;">Back to the marginal probability</a></li>
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<!-- navigation toc: --> <li><a href="#diffusion-models-for-hierarchical-vae-from-url-https-arxiv-org-abs-2208-11970" style="font-size: 80%;">Diffusion models for hierarchical VAE, from URL:"https://arxiv.org/abs/2208.11970"</a></li>
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<!-- navigation toc: --> <li><a href="#equation-for-the-markovian-hierarchical-vae" style="font-size: 80%;">Equation for the Markovian hierarchical VAE</a></li>
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<!-- navigation toc: --> <li><a href="#variational-diffusion-models" style="font-size: 80%;">Variational Diffusion Models</a></li>
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<!-- navigation toc: --> <li><a href="#second-assumption" style="font-size: 80%;">Second assumption</a></li>
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<!-- navigation toc: --> <li><a href="#parameterizing-gaussian-encoder" style="font-size: 80%;">Parameterizing Gaussian encoder</a></li>
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<!-- navigation toc: --> <li><a href="#encoder-transitions" style="font-size: 80%;">Encoder transitions</a></li>
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<!-- navigation toc: --> <li><a href="#third-assumption" style="font-size: 80%;">Third assumption</a></li>
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<!-- navigation toc: --> <li><a href="#noisification" style="font-size: 80%;">Noisification</a></li>
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<!-- navigation toc: --> <li><a href="#diffusion-models-from-url-https-arxiv-org-abs-2208-11970" style="font-size: 80%;">Diffusion models, from URL:"https://arxiv.org/abs/2208.11970"</a></li>
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<!-- navigation toc: --> <li><a href="#gaussian-modeling" style="font-size: 80%;">Gaussian modeling</a></li>
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<!-- navigation toc: --> <li><a href="#optimizing-the-variational-diffusion-model" style="font-size: 80%;">Optimizing the variational diffusion model</a></li>
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<!-- navigation toc: --> <li><a href="#continues" style="font-size: 80%;">Continues</a></li>
@@ -1373,9 +1363,10 @@ <h2 id="diffusion-learning" class="anchor">Diffusion learning </h2>
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<h2 id="mathematics-of-diffusion-models" class="anchor">Mathematics of diffusion models </h2>
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<p>Let us go back our discussions of the variational autoencoders from
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last week, see
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<a href="https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb" target="_self"><tt>https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb</tt></a>. As
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a first attempt at understanding diffusion models, we can think of
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last week and above.
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</p>
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<p>As a first attempt at understanding diffusion models, we can think of
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these as stacked VAEs, or better, recursive VAEs.
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</p>
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@@ -1438,15 +1429,6 @@ <h2 id="diffusion-models-for-hierarchical-vae-from-url-https-arxiv-org-abs-2208-
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\( \boldsymbol{h}_{t+1} \). Here \( \boldsymbol{z} \) is our latent variable \( \boldsymbol{h} \).
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</p>
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<br/><br/>
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<center>
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<p><img src="figures/figure1.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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<!-- !split -->
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<h2 id="equation-for-the-markovian-hierarchical-vae" class="anchor">Equation for the Markovian hierarchical VAE </h2>
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<p>We obtain then</p>
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$$
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\begin{align*}
@@ -1553,15 +1535,6 @@ <h2 id="noisification" class="anchor">Noisification </h2>
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identical to pure Gaussian noise. See figure on next slide.
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</p>
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<!-- !split -->
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<h2 id="diffusion-models-from-url-https-arxiv-org-abs-2208-11970" class="anchor">Diffusion models, from <a href="https://arxiv.org/abs/2208.11970" target="_self"><tt>https://arxiv.org/abs/2208.11970</tt></a> </h2>
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<br/><br/>
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<center>
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<p><img src="figures/figure2.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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<!-- !split -->
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<h2 id="gaussian-modeling" class="anchor">Gaussian modeling </h2>
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<p>For more details and implementaions, see Calvin Luo at <a href="https://arxiv.org/abs/2208.11970" target="_self"><tt>https://arxiv.org/abs/2208.11970</tt></a></p>
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<!-- FIGURE: [figures/figure4.png, width=800 frac=1.0] -->
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<p>The plans for the rest of the semester are</p>
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<ol>
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<li> May 1: public holiday</li>
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<li> May 8: More on diffusion models and introduction to GANs. Project work</li>
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<li> May 15: GANS and summary of course. Project work. This could also be the last lecture</li>
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<li> May 22: Alternatively, we could discuss briefly reinforcement learning and do a summary of the course. Project work.</li>
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</ol>
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<!-- ------------------- end of main content --------------- -->
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</div> <!-- end container -->
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<!-- include javascript, jQuery *first* -->

‎doc/pub/week13/html/week13-reveal.html‎

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@@ -1352,9 +1352,10 @@ <h2 id="diffusion-learning">Diffusion learning </h2>
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<h2 id="mathematics-of-diffusion-models">Mathematics of diffusion models </h2>
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<p>Let us go back our discussions of the variational autoencoders from
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last week, see
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<a href="https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb" target="_blank"><tt>https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb</tt></a>. As
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a first attempt at understanding diffusion models, we can think of
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last week and above.
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</p>
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<p>As a first attempt at understanding diffusion models, we can think of
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these as stacked VAEs, or better, recursive VAEs.
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</p>
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\( \boldsymbol{h}_{t+1} \). Here \( \boldsymbol{z} \) is our latent variable \( \boldsymbol{h} \).
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</p>
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<br/><br/>
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<center>
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<p><img src="figures/figure1.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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</section>
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<section>
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<h2 id="equation-for-the-markovian-hierarchical-vae">Equation for the Markovian hierarchical VAE </h2>
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<p>We obtain then</p>
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<p>&nbsp;<br>
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$$
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</p>
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</section>
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<section>
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<h2 id="diffusion-models-from-url-https-arxiv-org-abs-2208-11970">Diffusion models, from <a href="https://arxiv.org/abs/2208.11970" target="_blank"><tt>https://arxiv.org/abs/2208.11970</tt></a> </h2>
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<br/><br/>
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<center>
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<p><img src="figures/figure2.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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</section>
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<section>
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<h2 id="gaussian-modeling">Gaussian modeling </h2>
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<p>For more details and implementaions, see Calvin Luo at <a href="https://arxiv.org/abs/2208.11970" target="_blank"><tt>https://arxiv.org/abs/2208.11970</tt></a></p>
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<!-- FIGURE: [figures/figure4.png, width=800 frac=1.0] -->
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<p>The plans for the rest of the semester are</p>
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<ol>
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<p><li> May 1: public holiday</li>
1648+
<p><li> May 8: More on diffusion models and introduction to GANs. Project work</li>
1649+
<p><li> May 15: GANS and summary of course. Project work. This could also be the last lecture</li>
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<p><li> May 22: Alternatively, we could discuss briefly reinforcement learning and do a summary of the course. Project work.</li>
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</ol>
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</section>
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‎doc/pub/week13/html/week13-solarized.html‎

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'diffusion-models-for-hierarchical-vae-from-url-https-arxiv-org-abs-2208-11970'),
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('Equation for the Markovian hierarchical VAE',
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2,
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None,
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'equation-for-the-markovian-hierarchical-vae'),
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('Variational Diffusion Models',
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None,
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('Encoder transitions', 2, None, 'encoder-transitions'),
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('Third assumption', 2, None, 'third-assumption'),
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('Noisification', 2, None, 'noisification'),
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('Diffusion models, from URL:"https://arxiv.org/abs/2208.11970"',
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2,
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None,
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'diffusion-models-from-url-https-arxiv-org-abs-2208-11970'),
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('Gaussian modeling', 2, None, 'gaussian-modeling'),
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('Optimizing the variational diffusion model',
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2,
@@ -1304,9 +1296,10 @@ <h2 id="diffusion-learning">Diffusion learning </h2>
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<h2 id="mathematics-of-diffusion-models">Mathematics of diffusion models </h2>
13051297

13061298
<p>Let us go back our discussions of the variational autoencoders from
1307-
last week, see
1308-
<a href="https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb" target="_blank"><tt>https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb</tt></a>. As
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a first attempt at understanding diffusion models, we can think of
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last week and above.
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</p>
1301+
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<p>As a first attempt at understanding diffusion models, we can think of
13101303
these as stacked VAEs, or better, recursive VAEs.
13111304
</p>
13121305

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\( \boldsymbol{h}_{t+1} \). Here \( \boldsymbol{z} \) is our latent variable \( \boldsymbol{h} \).
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</p>
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<br/><br/>
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<center>
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<p><img src="figures/figure1.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="equation-for-the-markovian-hierarchical-vae">Equation for the Markovian hierarchical VAE </h2>
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<p>We obtain then</p>
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$$
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\begin{align*}
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identical to pure Gaussian noise. See figure on next slide.
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</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="diffusion-models-from-url-https-arxiv-org-abs-2208-11970">Diffusion models, from <a href="https://arxiv.org/abs/2208.11970" target="_blank"><tt>https://arxiv.org/abs/2208.11970</tt></a> </h2>
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<br/><br/>
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<center>
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<p><img src="figures/figure2.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="gaussian-modeling">Gaussian modeling </h2>
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15851560
<p>For more details and implementaions, see Calvin Luo at <a href="https://arxiv.org/abs/2208.11970" target="_blank"><tt>https://arxiv.org/abs/2208.11970</tt></a></p>
15861561

1587-
<!-- FIGURE: [figures/figure4.png, width=800 frac=1.0] -->
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<p>The plans for the rest of the semester are</p>
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<ol>
1564+
<li> May 1: public holiday</li>
1565+
<li> May 8: More on diffusion models and introduction to GANs. Project work</li>
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<li> May 15: GANS and summary of course. Project work. This could also be the last lecture</li>
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<li> May 22: Alternatively, we could discuss briefly reinforcement learning and do a summary of the course. Project work.</li>
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</ol>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license

‎doc/pub/week13/html/week13.html‎

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None,
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'diffusion-models-for-hierarchical-vae-from-url-https-arxiv-org-abs-2208-11970'),
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('Equation for the Markovian hierarchical VAE',
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2,
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None,
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'equation-for-the-markovian-hierarchical-vae'),
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('Variational Diffusion Models',
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2,
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None,
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('Encoder transitions', 2, None, 'encoder-transitions'),
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('Third assumption', 2, None, 'third-assumption'),
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('Noisification', 2, None, 'noisification'),
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('Diffusion models, from URL:"https://arxiv.org/abs/2208.11970"',
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2,
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None,
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'diffusion-models-from-url-https-arxiv-org-abs-2208-11970'),
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('Gaussian modeling', 2, None, 'gaussian-modeling'),
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('Optimizing the variational diffusion model',
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2,
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13811373
<h2 id="mathematics-of-diffusion-models">Mathematics of diffusion models </h2>
13821374

13831375
<p>Let us go back our discussions of the variational autoencoders from
1384-
last week, see
1385-
<a href="https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb" target="_blank"><tt>https://github.com/CompPhysics/AdvancedMachineLearning/blob/main/doc/pub/week12/ipynb/week12.ipynb</tt></a>. As
1386-
a first attempt at understanding diffusion models, we can think of
1376+
last week and above.
1377+
</p>
1378+
1379+
<p>As a first attempt at understanding diffusion models, we can think of
13871380
these as stacked VAEs, or better, recursive VAEs.
13881381
</p>
13891382

@@ -1446,15 +1439,6 @@ <h2 id="diffusion-models-for-hierarchical-vae-from-url-https-arxiv-org-abs-2208-
14461439
\( \boldsymbol{h}_{t+1} \). Here \( \boldsymbol{z} \) is our latent variable \( \boldsymbol{h} \).
14471440
</p>
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<br/><br/>
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<center>
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<p><img src="figures/figure1.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="equation-for-the-markovian-hierarchical-vae">Equation for the Markovian hierarchical VAE </h2>
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<p>We obtain then</p>
14591443
$$
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\begin{align*}
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15591543
identical to pure Gaussian noise. See figure on next slide.
15601544
</p>
15611545

1562-
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="diffusion-models-from-url-https-arxiv-org-abs-2208-11970">Diffusion models, from <a href="https://arxiv.org/abs/2208.11970" target="_blank"><tt>https://arxiv.org/abs/2208.11970</tt></a> </h2>
1564-
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<br/><br/>
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<center>
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<p><img src="figures/figure2.png" width="800" align="bottom"></p>
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</center>
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<br/><br/>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="gaussian-modeling">Gaussian modeling </h2>
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<p>For more details and implementaions, see Calvin Luo at <a href="https://arxiv.org/abs/2208.11970" target="_blank"><tt>https://arxiv.org/abs/2208.11970</tt></a></p>
16631638

1664-
<!-- FIGURE: [figures/figure4.png, width=800 frac=1.0] -->
1665-
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<p>The plans for the rest of the semester are</p>
1640+
<ol>
1641+
<li> May 1: public holiday</li>
1642+
<li> May 8: More on diffusion models and introduction to GANs. Project work</li>
1643+
<li> May 15: GANS and summary of course. Project work. This could also be the last lecture</li>
1644+
<li> May 22: Alternatively, we could discuss briefly reinforcement learning and do a summary of the course. Project work.</li>
1645+
</ol>
16661646
<!-- ------------------- end of main content --------------- -->
16671647
<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license

‎doc/pub/week13/ipynb/ipynb-week13-src.tar.gz‎

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