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fix(schedulers): promote DEIS polynomial coefficients to float64 to prevent catastrophic cancellation #15159

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fix(schedulers): promote DEIS polynomial coefficients to float64 to prevent catastrophic cancellation #15159

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26 changes: 14 additions & 12 deletions src/diffusers/schedulers/scheduling_deis_multistep.py
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Original file line number Diff line number Diff line change
Expand Up @@ -752,10 +752,11 @@ def multistep_deis_second_order_update(

m0, m1 = model_output_list[-1], model_output_list[-2]

# Convert to float64 scalars to avoid catastrophic cancellation in polynomial coefficients (#15090)
rho_t, rho_s0, rho_s1 = (
sigma_t / alpha_t,
sigma_s0 / alpha_s0,
sigma_s1 / alpha_s1,
float(sigma_t / alpha_t),
float(sigma_s0 / alpha_s0),
float(sigma_s1 / alpha_s1),
)

if self.config.algorithm_type == "deis":
Expand All @@ -764,8 +765,8 @@ def ind_fn(t, b, c):
# Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}]
return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c))

coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1)
coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0)
coef1 = float(ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1))
coef2 = float(ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0))

x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1)
return x_t
Expand Down Expand Up @@ -828,11 +829,12 @@ def multistep_deis_third_order_update(

m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]

# Convert to float64 scalars to avoid catastrophic cancellation in polynomial coefficients (#15090)
rho_t, rho_s0, rho_s1, rho_s2 = (
sigma_t / alpha_t,
sigma_s0 / alpha_s0,
sigma_s1 / alpha_s1,
sigma_s2 / alpha_s2,
float(sigma_t / alpha_t),
float(sigma_s0 / alpha_s0),
float(sigma_s1 / alpha_s1),
float(sigma_s2 / alpha_s2),
)

if self.config.algorithm_type == "deis":
Expand All @@ -850,9 +852,9 @@ def ind_fn(t, b, c, d):
denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d))
return numerator / denominator

coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2)
coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0)
coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1)
coef1 = float(ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2))
coef2 = float(ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0))
coef3 = float(ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1))

x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1 + coef3 * m2)

Expand Down
18 changes: 18 additions & 0 deletions tests/schedulers/test_scheduler_deis.py
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Original file line number Diff line number Diff line change
Expand Up @@ -271,3 +271,21 @@ def test_beta_sigmas(self):

def test_exponential_sigmas(self):
self.check_over_configs(use_exponential_sigmas=True)

def test_high_step_coefficient_precision(self):
# Regression test for #15090: DEIS coefficient precision causes increasing error as inference steps increase
for solver_order in [2, 3]:
scheduler = DEISMultistepScheduler(solver_order=solver_order)
for steps in [50, 100]:

@ZihaoW123 ZihaoW123 Nov 3, 2026

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Could the regression include the reported 500-step case with a time-varying model output? Constant epsilon combines the multistep coefficients, allowing individual coefficient errors to cancel, so it is a weak check of the polynomial cancellation being fixed.

scheduler.set_timesteps(steps)
rho0 = float(scheduler.sigmas[0])
sample = torch.full((1, 1), rho0 / (1 + rho0**2) ** 0.5, dtype=torch.float64)
constant = sample.item() * (1 + rho0**2) ** 0.5 - rho0
epsilon = torch.ones_like(sample)
for t in scheduler.timesteps:
sample = scheduler.step(epsilon, t, sample).prev_sample

rho = float(scheduler.sigmas[-1])
expected = (constant + rho) / (1 + rho**2) ** 0.5
assert sample.dtype == torch.float64
assert abs(sample.item() - expected) < 1e-4
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