diff --git a/src/cdp.jl b/src/cdp.jl
index 2441875..be5c1f8 100644
--- a/src/cdp.jl
+++ b/src/cdp.jl
@@ -603,12 +603,13 @@ function policy_iteration_operator!(cdp::ContinuousDP, C::Vector{Float64},
 end
 
 
-# Sup distance between two arrays, without allocating a temporary
+# Sup distance between two arrays, without allocating a temporary.
+# NaN entries propagate to the result (as with `maximum(abs, x - y)`), so
+# that a diverged iteration is never mistaken for a converged one.
 function _max_abs_diff(x, y)
     err = abs(zero(promote_type(eltype(x), eltype(y))))
     @inbounds for i in eachindex(x, y)
-        d = abs(x[i] - y[i])
-        d > err && (err = d)
+        err = max(err, abs(x[i] - y[i]))
     end
     return err
 end
diff --git a/test/test_workspace.jl b/test/test_workspace.jl
index 5fd7fdc..63dffeb 100644
--- a/test/test_workspace.jl
+++ b/test/test_workspace.jl
@@ -1,4 +1,22 @@
-using ContinuousDPs: CDPWorkspace, bellman_operator!, policy_iteration_operator!
+using ContinuousDPs: CDPWorkspace, bellman_operator!, policy_iteration_operator!,
+                     _max_abs_diff, operator_iteration!
+
+@testset "_max_abs_diff" begin
+    @test _max_abs_diff([1.0, 2.0], [1.5, 0.5]) == 1.5
+    @test _max_abs_diff([0.0], [0.0]) == 0.0
+    # NaN must propagate: a diverged iteration (Inf - Inf = NaN) must not be
+    # reported as converged
+    @test isnan(_max_abs_diff([NaN], [NaN]))
+    @test isnan(_max_abs_diff([1.0, NaN, 2.0], [1.0, NaN, 0.0]))
+    @test isnan(_max_abs_diff([Inf], [Inf]))
+
+    # End-to-end: an operator that diverges to non-finite values must not be
+    # declared converged
+    diverge!(C) = (C .= NaN; C)
+    converged, num_iter =
+        operator_iteration!(diverge!, [0.0, 0.0], 1e-8, 10, verbose=0)
+    @test !converged
+end
 
 @testset "CDPWorkspace" begin
     beta = 0.95