Answers.Body: <p>If you read the paper <a href="https://arxiv.org/pdf/2112.10752.pdf" rel="nofollow noreferrer">High-Resolution Image Synthesis with Latent Diffusion Models</a>, you'll notice that the Gaussian is actually <span class="math-container">$q(x_{t-1}|x_t, x_0)$</span>, whereas <span class="math-container">$q(x_{t-1}|x_t)$</span> is intractable. In this case, even if we know the appropriate distribution, we do not know <span class="math-container">$x_0$</span> in the denoising step (as that is ultimately what we are trying to predict) and hence we still have to approximate the posterior with some neural network approximation <span class="math-container">$p_{\theta}(x_{t-1}|x_t)$</span>.</p>
  
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Answers.CreationDate: 2024-02-03T04:18:47.917Z
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Body: <p>I recently learnt about the <em>diffusion model</em> in deep learning, can someone explain to me if we can induce noise to an input data and make it a gaussian like data, why can't we use the same process in reverse without training a network for denoising to deconstruct the gaussian data to the real image?</p>
  <p>in other words, in <span class="math-container">$q(x_{t-1}|x_t) q(x_t) = q(x_{t-1})q(x_{t}|x_{t-1})$</span> we do have <span class="math-container">$q(x_t)$</span> at the very last step which has become an gaussian through introducing noise in iterative manner, and we know what conditional probabilities are, why we try to approximate <span class="math-container">$q(x_{t-1}|x_t)$</span>, if it just a gaussian.</p>
  
Tags: <deep-learning><diffusion-models>
Title: Why learning with backward process is need in diffusion model despite knowing $q(x_{t-1}|x_t)$
UserDisplayName: aaa
ThreadText: # Why learning with backward process is need in diffusion model despite knowing $q(x_{t-1}|x_t)$
  
  (Asked by: username_0 on 2023-05-08)
  
  I recently learnt about the *diffusion model* in deep learning, can someone explain to me if we can induce noise to an input data and make it a gaussian like data, why can't we use the same process in reverse without training a network for denoising to deconstruct the gaussian data to the real image?
  
  in other words, in $q(x\_{t-1}|x\_t) q(x\_t) = q(x\_{t-1})q(x\_{t}|x\_{t-1})$ we do have $q(x\_t)$ at the very last step which has become an gaussian through introducing noise in iterative manner, and we know what conditional probabilities are, why we try to approximate $q(x\_{t-1}|x\_t)$, if it just a gaussian.
  
  **Tags:** deep-learning, diffusion-models
  
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  ## 1 answers
  
  ### Answer by username_1 on 2024-02-03. Score: 2
  
  If you read the paper [High-Resolution Image Synthesis with Latent Diffusion Models](https://arxiv.org/pdf/2112.10752.pdf), you'll notice that the Gaussian is actually $q(x\_{t-1}|x\_t, x\_0)$, whereas $q(x\_{t-1}|x\_t)$ is intractable. In this case, even if we know the appropriate distribution, we do not know $x\_0$ in the denoising step (as that is ultimately what we are trying to predict) and hence we still have to approximate the posterior with some neural network approximation $p\_{\theta}(x\_{t-1}|x\_t)$.
  
  
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