diff --git a/src/inference/baum_welch.jl b/src/inference/baum_welch.jl
index 1bc2566..816af8a 100644
--- a/src/inference/baum_welch.jl
+++ b/src/inference/baum_welch.jl
@@ -1,13 +1,19 @@
 function baum_welch_has_converged(
-    logL_evolution::Vector; atol::Real, loglikelihood_increasing::Bool
+    logL_evolution::Vector; atol::Real, loglikelihood_increasing::Bool, stopping_criterion::Symbol
 )
     if length(logL_evolution) >= 2
         logL, logL_prev = logL_evolution[end], logL_evolution[end - 1]
         progress = logL - logL_prev
-        if loglikelihood_increasing && progress < min(0, -atol)
-            error("Loglikelihood decreased in Baum-Welch")
-        elseif progress < atol
-            return true
+        if stopping_criterion == :convergence
+            if loglikelihood_increasing && progress < min(0, -atol)
+                error("Loglikelihood decreased in Baum-Welch")
+            elseif progress < atol
+                return true
+            end
+        elseif stopping_criterion == :stability
+            if abs(progress) < atol
+                return true
+            end
         end
     end
     return false
@@ -26,12 +32,13 @@ function baum_welch!(
     atol::Real,
     max_iterations::Integer,
     loglikelihood_increasing::Bool,
+    stopping_criterion::Symbol
 )
     for _ in 1:max_iterations
         forward_backward!(fb_storage, hmm, obs_seq, control_seq; seq_ends)
         push!(logL_evolution, logdensityof(hmm) + sum(fb_storage.logL))
         fit!(hmm, fb_storage, obs_seq, control_seq; seq_ends)
-        if baum_welch_has_converged(logL_evolution; atol, loglikelihood_increasing)
+        if baum_welch_has_converged(logL_evolution; atol, loglikelihood_increasing, stopping_criterion)
             break
         end
     end
@@ -50,6 +57,7 @@ Return a tuple `(hmm_est, loglikelihood_evolution)` where `hmm_est` is the estim
 - `atol`: minimum loglikelihood increase at an iteration of the algorithm (otherwise the algorithm is deemed to have converged)
 - `max_iterations`: maximum number of iterations of the algorithm
 - `loglikelihood_increasing`: whether to throw an error if the loglikelihood decreases
+- `stopping_criterion`: The stopping criterion (either `:convergence` or `:stability`).
 """
 function baum_welch(
     hmm_guess::AbstractHMM,
@@ -59,6 +67,7 @@ function baum_welch(
     atol=1e-5,
     max_iterations=100,
     loglikelihood_increasing=true,
+    stopping_criterion::Symbol=:convergence
 )
     hmm = deepcopy(hmm_guess)
     fb_storage = initialize_forward_backward(hmm, obs_seq, control_seq; seq_ends)
@@ -74,6 +83,7 @@ function baum_welch(
         atol,
         max_iterations,
         loglikelihood_increasing=false,
+        stopping_criterion=stopping_criterion
     )
     return hmm, logL_evolution
 end
diff --git a/src/types/abstract_hmm.jl b/src/types/abstract_hmm.jl
index 6f3f8e5..bb05ca9 100644
--- a/src/types/abstract_hmm.jl
+++ b/src/types/abstract_hmm.jl
@@ -128,6 +128,8 @@ function obs_logdensities!(
     @inbounds @simd for i in eachindex(logb, dists)
         logb[i] = logdensityof(dists[i], obs)
     end
+    logb[findall(i -> i < -log(-nextfloat(-Inf)), logb)] .= -log(-nextfloat(-Inf))
+    logb[findall(i -> i > log(prevfloat(Inf)), logb)] .= log(prevfloat(Inf))
     @argcheck maximum(logb) < typemax(T)
     return nothing
 end