Fix Beta sampling to match the paper

We need a beta distribution of timesteps, not sigmas. Also allow
distribution parameters > 1.

Author: heftig

modules/sd_schedulers.py

@@ -116,15 +116,25 @@ def ddim_scheduler(n, sigma_min, sigma_max, inner_model, device):
     return torch.FloatTensor(sigs).to(device)
 
 
-def beta_scheduler(n, sigma_min, sigma_max, inner_model, device):
-    # From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024) """
+def beta_scheduler(n, sigma_min, sigma_max, inner_model, device, sgm=False):
+    start = inner_model.sigma_to_t(torch.tensor(sigma_max))
+    end = inner_model.sigma_to_t(torch.tensor(sigma_min))
+
+    # From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)
     alpha = shared.opts.beta_dist_alpha
     beta = shared.opts.beta_dist_beta
-    timesteps = 1 - np.linspace(0, 1, n)
+    if sgm:
+        timesteps = np.linspace(1, 0, n + 1)[:-1]
+    else:
+        timesteps = np.linspace(1, 0, n)
     timesteps = [stats.beta.ppf(x, alpha, beta) for x in timesteps]
-    sigmas = [sigma_min + (x * (sigma_max-sigma_min)) for x in timesteps]
-    sigmas += [0.0]
-    return torch.FloatTensor(sigmas).to(device)
+
+    sigs = []
+    for x in range(len(timesteps)):
+        ts = end + (timesteps[x] * (start - end))
+        sigs.append(inner_model.t_to_sigma(ts))
+    sigs += [0.0]
+    return torch.FloatTensor(sigs).to(device)
 
 
 schedulers = [

modules/shared_options.py

@@ -407,8 +407,8 @@
     'uni_pc_lower_order_final': OptionInfo(True, "UniPC lower order final", infotext='UniPC lower order final'),
     'sd_noise_schedule': OptionInfo("Default", "Noise schedule for sampling", gr.Radio, {"choices": ["Default", "Zero Terminal SNR"]}, infotext="Noise Schedule").info("for use with zero terminal SNR trained models"),
     'skip_early_cond': OptionInfo(0.0, "Ignore negative prompt during early sampling", gr.Slider, {"minimum": 0.0, "maximum": 1.0, "step": 0.01}, infotext="Skip Early CFG").info("disables CFG on a proportion of steps at the beginning of generation; 0=skip none; 1=skip all; can both improve sample diversity/quality and speed up sampling; XYZ plot: Skip Early CFG"),
-    'beta_dist_alpha': OptionInfo(0.6, "Beta scheduler - alpha", gr.Slider, {"minimum": 0.01, "maximum": 1.0, "step": 0.01}, infotext='Beta scheduler alpha').info('Default = 0.6; the alpha parameter of the beta distribution used in Beta sampling'),
-    'beta_dist_beta': OptionInfo(0.6, "Beta scheduler - beta", gr.Slider, {"minimum": 0.01, "maximum": 1.0, "step": 0.01}, infotext='Beta scheduler beta').info('Default = 0.6; the beta parameter of the beta distribution used in Beta sampling'),
+    'beta_dist_alpha': OptionInfo(0.6, "Beta scheduler - alpha", gr.Slider, {"minimum": 0.01, "maximum": 5.0, "step": 0.01}, infotext='Beta scheduler alpha').info('Default = 0.6; the alpha parameter of the beta distribution used in Beta sampling'),
+    'beta_dist_beta': OptionInfo(0.6, "Beta scheduler - beta", gr.Slider, {"minimum": 0.01, "maximum": 5.0, "step": 0.01}, infotext='Beta scheduler beta').info('Default = 0.6; the beta parameter of the beta distribution used in Beta sampling'),
 }))
 
 options_templates.update(options_section(('postprocessing', "Postprocessing", "postprocessing"), {