How to smoothly interpolate between two distributions?

[imxtx]

Hi there, I'm using the ot.unbalanced.barycenter_unbalanced function to interpolate between two curves. However, I found some unsmooth interpolants between the source and the target (marked by squares in the figure below).

I want to transform the source curve to the target curve smoothly without producing these sawteeth. How should I achieve this?

Here is my code:

# Positions
x = np.arange(len(src)).reshape(-1, 1)  # shape: [F, 1]
n_bins = len(src)

# Cost matrix: squared Euclidean distance
C = ot.utils.dist(x, x, metric='sqeuclidean')

# Input distributions
a = src.copy() # shape: (100,)
b = tgt.copy() # shape: (100,)

# Stack them into a matrix: [n_bins, n_distributions]
distributions = np.stack([a, b], axis=1)  # shape: [F, 2]

# Weights for interpolation (e.g. t=0.3 → 30% a + 70% b)
t_values = np.linspace(0.1, 0.9, 5)
colors = ['g', 'c', 'm', 'y', 'k']

# Plot original
plt.figure(figsize=(10, 6))
plt.plot(x, 10 * np.log10(a), 'b', label='Source distribution')
plt.plot(x, 10 * np.log10(b), 'r', label='Target distribution')

for t, color in zip(t_values, colors):
    weights = np.array([1 - t, t])

    # Compute unbalanced barycenter
    barycenter = ot.unbalanced.barycenter_unbalanced(
        distributions, C, reg=1e-1, reg_m=10, weights=weights
    )  # shape: [F,]

    plt.plot(x, 10 * np.log10(barycenter), color=color, label=f"t={t:.1f}")

plt.title("Unbalanced OT Barycentric Interpolation (POT)")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()