fixed forward diffusion formula

app.py

@@ -387,8 +387,8 @@ with gr.Blocks(title="Diffusion — A DDPM in motion", **BLOCK_OPTIONS) as demo:
         forward_noise = gr.State(None)
         with gr.Column(elem_classes=["lab-panel", "process-panel"]):
             gr.HTML('<div class="process-heading"><h2>Forward process: image to noise</h2>'
-                    '<span class="equation">x<sub>t</sub> = √α<sub>t</sub> x<sub>t−1</sub>'
-                    ' + √(1 − α<sub>t</sub>) ε<sub>t</sub></span></div>')
+                    '<span class="equation">x<sub>t</sub> = √α̅<sub>t</sub> x<sub>t−1</sub>'
+                    ' + √(1 − α̅<sub>t</sub>) ε<sub>t</sub></span></div>')
             with gr.Row(elem_classes="process-toolbar"):
                 diffuse_button = gr.Button("Diffuse", elem_classes="process-button")
                 forward_status = gr.HTML(value=progress_html(), container=False,

index.html

@@ -44,7 +44,7 @@
         <div class="process-heading"><div class="panel-heading"><div>
 							<h2 id="diffusion-title">Forward process: image to noise</h2>
 					</div></div>
-					<span class="equation">x<sub>t</sub> = √α<sub>t</sub> x<sub>t−1</sub> + √(1 − α<sub>t</sub>) ε<sub>t</sub></span>
+					<span class="equation">x<sub>t</sub> = √α̅<sub>t</sub> x<sub>0</sub> + √(1 − α̅<sub>t</sub>) ε</span>
 				</div>
         <output id="forward-progress-label" class="step-progress">0/1000</output>
         <div id="diffusion-track" class="image-track" aria-label="Forward diffusion checkpoints"></div>